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https://github.com/ZDoom/Raze.git
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1802 lines
40 KiB
C++
1802 lines
40 KiB
C++
/*
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** vectors.h
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** Vector math routines.
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**
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**---------------------------------------------------------------------------
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** Copyright 2005-2007 Randy Heit
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** All rights reserved.
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**
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** Redistribution and use in source and binary forms, with or without
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** modification, are permitted provided that the following conditions
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** are met:
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**
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** 1. Redistributions of source code must retain the above copyright
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** notice, this list of conditions and the following disclaimer.
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** 2. Redistributions in binary form must reproduce the above copyright
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** notice, this list of conditions and the following disclaimer in the
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** documentation and/or other materials provided with the distribution.
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** 3. The name of the author may not be used to endorse or promote products
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** derived from this software without specific prior written permission.
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**
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** THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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** IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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** OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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** IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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** NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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** DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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** THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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** (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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** THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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**---------------------------------------------------------------------------
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**
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** Since C++ doesn't let me add completely new operators, the following two
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** are overloaded for vectors:
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**
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** | dot product
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** ^ cross product
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*/
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#ifndef VECTORS_H
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#define VECTORS_H
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#include <cstddef>
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#include <math.h>
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#include <float.h>
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#include <string.h>
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#include "xs_Float.h"
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#include "math/cmath.h"
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#include "basics.h"
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#include "cmdlib.h"
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#define EQUAL_EPSILON (1/65536.)
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// make this a local inline function to avoid any dependencies on other headers and not pollute the global namespace
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namespace pi
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{
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inline constexpr double pi() { return 3.14159265358979323846; }
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inline constexpr double pif() { return 3.14159265358979323846f; }
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}
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template<class vec_t> struct TVector3;
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template<class vec_t> struct TRotator;
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template<class vec_t> struct TAngle;
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template<class vec_t>
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struct TVector2
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{
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vec_t X, Y;
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TVector2() = default;
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TVector2 (vec_t a, vec_t b)
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: X(a), Y(b)
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{
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}
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TVector2(const TVector2 &other) = default;
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TVector2 (const TVector3<vec_t> &other) // Copy the X and Y from the 3D vector and discard the Z
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: X(other.X), Y(other.Y)
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{
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}
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TVector2(vec_t *o)
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: X(o[0]), Y(o[1])
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{
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}
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void Zero()
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{
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Y = X = 0;
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}
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bool isZero() const
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{
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return X == 0 && Y == 0;
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}
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TVector2 &operator= (const TVector2 &other) = default;
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// Access X and Y as an array
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vec_t &operator[] (int index)
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{
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return index == 0 ? X : Y;
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}
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const vec_t &operator[] (int index) const
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{
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return index == 0 ? X : Y;
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}
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// Test for equality
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bool operator== (const TVector2 &other) const
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{
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return X == other.X && Y == other.Y;
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}
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// Test for inequality
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bool operator!= (const TVector2 &other) const
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{
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return X != other.X || Y != other.Y;
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}
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// Test for approximate equality
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bool ApproximatelyEquals (const TVector2 &other) const
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{
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return fabs(X - other.X) < EQUAL_EPSILON && fabs(Y - other.Y) < EQUAL_EPSILON;
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}
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// Test for approximate inequality
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bool DoesNotApproximatelyEqual (const TVector2 &other) const
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{
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return fabs(X - other.X) >= EQUAL_EPSILON || fabs(Y - other.Y) >= EQUAL_EPSILON;
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}
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// Unary negation
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TVector2 operator- () const
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{
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return TVector2(-X, -Y);
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}
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// Scalar addition
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#if 0
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TVector2 &operator+= (double scalar)
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{
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X += scalar, Y += scalar;
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return *this;
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}
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#endif
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friend TVector2 operator+ (const TVector2 &v, vec_t scalar)
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{
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return TVector2(v.X + scalar, v.Y + scalar);
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}
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friend TVector2 operator+ (vec_t scalar, const TVector2 &v)
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{
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return TVector2(v.X + scalar, v.Y + scalar);
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}
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// Scalar subtraction
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TVector2 &operator-= (vec_t scalar)
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{
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X -= scalar, Y -= scalar;
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return *this;
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}
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TVector2 operator- (vec_t scalar) const
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{
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return TVector2(X - scalar, Y - scalar);
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}
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// Scalar multiplication
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TVector2 &operator*= (vec_t scalar)
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{
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X *= scalar, Y *= scalar;
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return *this;
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}
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friend TVector2 operator* (const TVector2 &v, vec_t scalar)
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{
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return TVector2(v.X * scalar, v.Y * scalar);
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}
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friend TVector2 operator* (vec_t scalar, const TVector2 &v)
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{
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return TVector2(v.X * scalar, v.Y * scalar);
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}
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// Scalar division
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TVector2 &operator/= (vec_t scalar)
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{
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scalar = 1 / scalar, X *= scalar, Y *= scalar;
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return *this;
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}
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TVector2 operator/ (vec_t scalar) const
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{
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scalar = 1 / scalar;
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return TVector2(X * scalar, Y * scalar);
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}
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// Vector addition
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TVector2 &operator+= (const TVector2 &other)
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{
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X += other.X, Y += other.Y;
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return *this;
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}
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TVector2 operator+ (const TVector2 &other) const
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{
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return TVector2(X + other.X, Y + other.Y);
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}
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// Vector subtraction
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TVector2 &operator-= (const TVector2 &other)
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{
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X -= other.X, Y -= other.Y;
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return *this;
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}
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TVector2 operator- (const TVector2 &other) const
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{
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return TVector2(X - other.X, Y - other.Y);
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}
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// Vector length
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vec_t Length() const
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{
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return (vec_t)g_sqrt (LengthSquared());
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}
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vec_t LengthSquared() const
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{
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return X*X + Y*Y;
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}
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double Sum() const
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{
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return abs(X) + abs(Y);
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}
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// Return a unit vector facing the same direction as this one
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TVector2 Unit() const
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{
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vec_t len = Length();
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if (len != 0) len = 1 / len;
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return *this * len;
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}
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// Scales this vector into a unit vector. Returns the old length
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vec_t MakeUnit()
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{
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vec_t len, ilen;
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len = ilen = Length();
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if (ilen != 0) ilen = 1 / ilen;
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*this *= ilen;
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return len;
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}
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// Resizes this vector to be the specified length (if it is not 0)
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TVector2 &MakeResize(double len)
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{
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double scale = len / Length();
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X = vec_t(X * scale);
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Y = vec_t(Y * scale);
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return *this;
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}
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TVector2 Resized(double len) const
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{
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double vlen = Length();
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if (vlen != 0.)
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{
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double scale = len / vlen;
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return{ vec_t(X * scale), vec_t(Y * scale) };
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}
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else
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{
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return *this;
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}
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}
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// Dot product
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vec_t operator | (const TVector2 &other) const
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{
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return X*other.X + Y*other.Y;
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}
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vec_t dot(const TVector2 &other) const
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{
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return X*other.X + Y*other.Y;
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}
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// Returns the angle that the ray (0,0)-(X,Y) faces
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TAngle<vec_t> Angle() const;
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// Returns a rotated vector. angle is in degrees.
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TVector2 Rotated (double angle) const
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{
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double cosval = g_cosdeg (angle);
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double sinval = g_sindeg (angle);
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return TVector2(X*cosval - Y*sinval, Y*cosval + X*sinval);
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}
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// Returns a rotated vector. angle is in degrees.
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template<class T>
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TVector2 Rotated(TAngle<T> angle) const
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{
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double cosval = angle.Cos();
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double sinval = angle.Sin();
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return TVector2(X*cosval - Y*sinval, Y*cosval + X*sinval);
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}
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// Returns a rotated vector. angle is in degrees.
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TVector2 Rotated(const double cosval, const double sinval) const
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{
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return TVector2(X*cosval - Y*sinval, Y*cosval + X*sinval);
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}
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// Returns a vector rotated 90 degrees clockwise.
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TVector2 Rotated90CW() const
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{
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return TVector2(Y, -X);
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}
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// Returns a vector rotated 90 degrees counterclockwise.
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TVector2 Rotated90CCW() const
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{
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return TVector2(-Y, X);
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}
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};
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template<class vec_t>
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struct TVector3
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{
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typedef TVector2<vec_t> Vector2;
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// this does not compile - should be true on all relevant hardware.
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//static_assert(myoffsetof(TVector3, X) == myoffsetof(Vector2, X) && myoffsetof(TVector3, Y) == myoffsetof(Vector2, Y), "TVector2 and TVector3 are not aligned");
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vec_t X, Y, Z;
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TVector3() = default;
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TVector3 (vec_t a, vec_t b, vec_t c)
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: X(a), Y(b), Z(c)
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{
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}
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TVector3(vec_t *o)
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: X(o[0]), Y(o[1]), Z(o[2])
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{
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}
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TVector3(std::nullptr_t nul) = delete;
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TVector3(const TVector3 &other) = default;
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TVector3 (const Vector2 &xy, vec_t z)
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: X(xy.X), Y(xy.Y), Z(z)
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{
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}
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TVector3 (const TRotator<vec_t> &rot);
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void Zero()
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{
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Z = Y = X = 0;
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}
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bool isZero() const
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{
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return X == 0 && Y == 0 && Z == 0;
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}
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TVector3 plusZ(double z) const
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{
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return { X, Y, Z + z };
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}
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TVector3 &operator= (const TVector3 &other) = default;
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// Access X and Y and Z as an array
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vec_t &operator[] (int index)
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{
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return index == 0 ? X : index == 1 ? Y : Z;
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}
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const vec_t &operator[] (int index) const
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{
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return index == 0 ? X : index == 1 ? Y : Z;
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}
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// Test for equality
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bool operator== (const TVector3 &other) const
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{
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return X == other.X && Y == other.Y && Z == other.Z;
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}
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// Test for inequality
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bool operator!= (const TVector3 &other) const
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{
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return X != other.X || Y != other.Y || Z != other.Z;
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}
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// Test for approximate equality
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bool ApproximatelyEquals (const TVector3 &other) const
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{
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return fabs(X - other.X) < EQUAL_EPSILON && fabs(Y - other.Y) < EQUAL_EPSILON && fabs(Z - other.Z) < EQUAL_EPSILON;
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}
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// Test for approximate inequality
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bool DoesNotApproximatelyEqual (const TVector3 &other) const
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{
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return fabs(X - other.X) >= EQUAL_EPSILON || fabs(Y - other.Y) >= EQUAL_EPSILON || fabs(Z - other.Z) >= EQUAL_EPSILON;
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}
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// Unary negation
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TVector3 operator- () const
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{
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return TVector3(-X, -Y, -Z);
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}
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// Scalar addition
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#if 0
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TVector3 &operator+= (vec_t scalar)
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{
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X += scalar, Y += scalar, Z += scalar;
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return *this;
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}
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#endif
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friend TVector3 operator+ (const TVector3 &v, vec_t scalar)
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{
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return TVector3(v.X + scalar, v.Y + scalar, v.Z + scalar);
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}
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friend TVector3 operator+ (vec_t scalar, const TVector3 &v)
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{
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return TVector3(v.X + scalar, v.Y + scalar, v.Z + scalar);
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}
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// Scalar subtraction
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TVector3 &operator-= (vec_t scalar)
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{
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X -= scalar, Y -= scalar, Z -= scalar;
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return *this;
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}
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TVector3 operator- (vec_t scalar) const
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{
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return TVector3(X - scalar, Y - scalar, Z - scalar);
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}
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// Scalar multiplication
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TVector3 &operator*= (vec_t scalar)
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{
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X = vec_t(X *scalar), Y = vec_t(Y * scalar), Z = vec_t(Z * scalar);
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return *this;
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}
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friend TVector3 operator* (const TVector3 &v, vec_t scalar)
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{
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return TVector3(v.X * scalar, v.Y * scalar, v.Z * scalar);
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}
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friend TVector3 operator* (vec_t scalar, const TVector3 &v)
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{
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return TVector3(v.X * scalar, v.Y * scalar, v.Z * scalar);
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}
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// Scalar division
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TVector3 &operator/= (vec_t scalar)
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{
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scalar = 1 / scalar, X = vec_t(X * scalar), Y = vec_t(Y * scalar), Z = vec_t(Z * scalar);
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return *this;
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}
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TVector3 operator/ (vec_t scalar) const
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{
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scalar = 1 / scalar;
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return TVector3(X * scalar, Y * scalar, Z * scalar);
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}
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// Vector addition
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TVector3 &operator+= (const TVector3 &other)
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{
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X += other.X, Y += other.Y, Z += other.Z;
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return *this;
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}
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TVector3 operator+ (const TVector3 &other) const
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{
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return TVector3(X + other.X, Y + other.Y, Z + other.Z);
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}
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// Vector subtraction
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TVector3 &operator-= (const TVector3 &other)
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{
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X -= other.X, Y -= other.Y, Z -= other.Z;
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return *this;
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}
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TVector3 operator- (const TVector3 &other) const
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{
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return TVector3(X - other.X, Y - other.Y, Z - other.Z);
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}
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// Add a 2D vector to this 3D vector, leaving Z unchanged.
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TVector3 &operator+= (const Vector2 &other)
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{
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X += other.X, Y += other.Y;
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return *this;
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}
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// Subtract a 2D vector from this 3D vector, leaving Z unchanged.
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TVector3 &operator-= (const Vector2 &other)
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{
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X -= other.X, Y -= other.Y;
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return *this;
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}
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// returns the XY fields as a 2D-vector.
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const Vector2& XY() const
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{
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return *reinterpret_cast<const Vector2*>(this);
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}
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Vector2& XY()
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{
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return *reinterpret_cast<Vector2*>(this);
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}
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// Add a 3D vector and a 2D vector.
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friend TVector3 operator+ (const TVector3 &v3, const Vector2 &v2)
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{
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return TVector3(v3.X + v2.X, v3.Y + v2.Y, v3.Z);
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}
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friend TVector3 operator- (const TVector3 &v3, const Vector2 &v2)
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{
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return TVector3(v3.X - v2.X, v3.Y - v2.Y, v3.Z);
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}
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friend Vector2 operator+ (const Vector2 &v2, const TVector3 &v3)
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{
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return Vector2(v2.X + v3.X, v2.Y + v3.Y);
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}
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// Subtract a 3D vector and a 2D vector.
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// Discards the Z component of the 3D vector and returns a 2D vector.
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friend Vector2 operator- (const TVector2<vec_t> &v2, const TVector3 &v3)
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{
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return Vector2(v2.X - v3.X, v2.Y - v3.Y);
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}
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void GetRightUp(TVector3 &right, TVector3 &up)
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{
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TVector3 n(X, Y, Z);
|
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TVector3 fn(fabs(n.X), fabs(n.Y), fabs(n.Z));
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int major = 0;
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|
|
if (fn[1] > fn[major]) major = 1;
|
|
if (fn[2] > fn[major]) major = 2;
|
|
|
|
// build right vector by hand
|
|
if (fabs(fn[0] - 1.0f) < FLT_EPSILON || fabs(fn[1] - 1.0f) < FLT_EPSILON || fabs(fn[2] - 1.0f) < FLT_EPSILON)
|
|
{
|
|
if (major == 0 && n[0] > 0.f)
|
|
{
|
|
right = { 0.f, 0.f, -1.f };
|
|
}
|
|
else if (major == 0)
|
|
{
|
|
right = { 0.f, 0.f, 1.f };
|
|
}
|
|
else if (major == 1 || (major == 2 && n[2] > 0.f))
|
|
{
|
|
right = { 1.f, 0.f, 0.f };
|
|
}
|
|
// Unconditional to ease static analysis
|
|
else // major == 2 && n[2] <= 0.0f
|
|
{
|
|
right = { -1.f, 0.f, 0.f };
|
|
}
|
|
}
|
|
else
|
|
{
|
|
static TVector3 axis[3] =
|
|
{
|
|
{ 1.0f, 0.0f, 0.0f },
|
|
{ 0.0f, 1.0f, 0.0f },
|
|
{ 0.0f, 0.0f, 1.0f }
|
|
};
|
|
|
|
right = axis[major] ^ n;
|
|
}
|
|
|
|
up = n ^right;
|
|
right.MakeUnit();
|
|
up.MakeUnit();
|
|
}
|
|
|
|
|
|
// Returns the angle (in radians) that the ray (0,0)-(X,Y) faces
|
|
TAngle<vec_t> Angle() const;
|
|
TAngle<vec_t> Pitch() const;
|
|
|
|
// Vector length
|
|
double Length() const
|
|
{
|
|
return g_sqrt (LengthSquared());
|
|
}
|
|
|
|
double LengthSquared() const
|
|
{
|
|
return X*X + Y*Y + Z*Z;
|
|
}
|
|
|
|
double Sum() const
|
|
{
|
|
return abs(X) + abs(Y) + abs(Z);
|
|
}
|
|
|
|
|
|
// Return a unit vector facing the same direction as this one
|
|
TVector3 Unit() const
|
|
{
|
|
double len = Length();
|
|
if (len != 0) len = 1 / len;
|
|
return *this * (vec_t)len;
|
|
}
|
|
|
|
// Scales this vector into a unit vector
|
|
void MakeUnit()
|
|
{
|
|
double len = Length();
|
|
if (len != 0) len = 1 / len;
|
|
*this *= (vec_t)len;
|
|
}
|
|
|
|
// Resizes this vector to be the specified length (if it is not 0)
|
|
TVector3 &MakeResize(double len)
|
|
{
|
|
double vlen = Length();
|
|
if (vlen != 0.)
|
|
{
|
|
double scale = len / vlen;
|
|
X = vec_t(X * scale);
|
|
Y = vec_t(Y * scale);
|
|
Z = vec_t(Z * scale);
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
TVector3 Resized(double len) const
|
|
{
|
|
double vlen = Length();
|
|
if (vlen != 0.)
|
|
{
|
|
double scale = len / vlen;
|
|
return{ vec_t(X * scale), vec_t(Y * scale), vec_t(Z * scale) };
|
|
}
|
|
else
|
|
{
|
|
return *this;
|
|
}
|
|
}
|
|
|
|
// Dot product
|
|
vec_t operator | (const TVector3 &other) const
|
|
{
|
|
return X*other.X + Y*other.Y + Z*other.Z;
|
|
}
|
|
|
|
vec_t dot (const TVector3& other) const
|
|
{
|
|
return X * other.X + Y * other.Y + Z * other.Z;
|
|
}
|
|
|
|
// Cross product
|
|
TVector3 operator ^ (const TVector3 &other) const
|
|
{
|
|
return TVector3(Y*other.Z - Z*other.Y,
|
|
Z*other.X - X*other.Z,
|
|
X*other.Y - Y*other.X);
|
|
}
|
|
|
|
TVector3 &operator ^= (const TVector3 &other)
|
|
{
|
|
*this = *this ^ other;
|
|
return *this;
|
|
}
|
|
};
|
|
|
|
template<class vec_t>
|
|
struct TVector4
|
|
{
|
|
typedef TVector2<vec_t> Vector2;
|
|
typedef TVector3<vec_t> Vector3;
|
|
|
|
vec_t X, Y, Z, W;
|
|
|
|
TVector4() = default;
|
|
|
|
TVector4(vec_t a, vec_t b, vec_t c, vec_t d)
|
|
: X(a), Y(b), Z(c), W(d)
|
|
{
|
|
}
|
|
|
|
TVector4(vec_t *o)
|
|
: X(o[0]), Y(o[1]), Z(o[2]), W(o[3])
|
|
{
|
|
}
|
|
|
|
TVector4(const TVector4 &other) = default;
|
|
|
|
TVector4(const Vector3 &xyz, vec_t w)
|
|
: X(xyz.X), Y(xyz.Y), Z(xyz.Z), W(w)
|
|
{
|
|
}
|
|
|
|
TVector4(const vec_t v[4])
|
|
: TVector4(v[0], v[1], v[2], v[3])
|
|
{
|
|
}
|
|
|
|
void Zero()
|
|
{
|
|
Z = Y = X = W = 0;
|
|
}
|
|
|
|
bool isZero() const
|
|
{
|
|
return X == 0 && Y == 0 && Z == 0 && W == 0;
|
|
}
|
|
|
|
TVector4 &operator= (const TVector4 &other) = default;
|
|
|
|
// Access X and Y and Z as an array
|
|
vec_t &operator[] (int index)
|
|
{
|
|
return (&X)[index];
|
|
}
|
|
|
|
const vec_t &operator[] (int index) const
|
|
{
|
|
return (&X)[index];
|
|
}
|
|
|
|
// Test for equality
|
|
bool operator== (const TVector4 &other) const
|
|
{
|
|
return X == other.X && Y == other.Y && Z == other.Z && W == other.W;
|
|
}
|
|
|
|
// Test for inequality
|
|
bool operator!= (const TVector4 &other) const
|
|
{
|
|
return X != other.X || Y != other.Y || Z != other.Z || W != other.W;
|
|
}
|
|
|
|
// returns the XY fields as a 2D-vector.
|
|
const Vector2& XY() const
|
|
{
|
|
return *reinterpret_cast<const Vector2*>(this);
|
|
}
|
|
|
|
Vector2& XY()
|
|
{
|
|
return *reinterpret_cast<Vector2*>(this);
|
|
}
|
|
|
|
// returns the XY fields as a 2D-vector.
|
|
const Vector3& XYZ() const
|
|
{
|
|
return *reinterpret_cast<const Vector3*>(this);
|
|
}
|
|
|
|
Vector3& XYZ()
|
|
{
|
|
return *reinterpret_cast<Vector3*>(this);
|
|
}
|
|
|
|
|
|
// Test for approximate equality
|
|
bool ApproximatelyEquals(const TVector4 &other) const
|
|
{
|
|
return fabs(X - other.X) < EQUAL_EPSILON && fabs(Y - other.Y) < EQUAL_EPSILON && fabs(Z - other.Z) < EQUAL_EPSILON && fabs(W - other.W) < EQUAL_EPSILON;
|
|
}
|
|
|
|
// Test for approximate inequality
|
|
bool DoesNotApproximatelyEqual(const TVector4 &other) const
|
|
{
|
|
return fabs(X - other.X) >= EQUAL_EPSILON || fabs(Y - other.Y) >= EQUAL_EPSILON || fabs(Z - other.Z) >= EQUAL_EPSILON || fabs(W - other.W) >= EQUAL_EPSILON;
|
|
}
|
|
|
|
// Unary negation
|
|
TVector4 operator- () const
|
|
{
|
|
return TVector4(-X, -Y, -Z, -W);
|
|
}
|
|
|
|
// Scalar addition
|
|
TVector4 &operator+= (vec_t scalar)
|
|
{
|
|
X += scalar, Y += scalar, Z += scalar; W += scalar;
|
|
return *this;
|
|
}
|
|
|
|
friend TVector4 operator+ (const TVector4 &v, vec_t scalar)
|
|
{
|
|
return TVector4(v.X + scalar, v.Y + scalar, v.Z + scalar, v.W + scalar);
|
|
}
|
|
|
|
friend TVector4 operator+ (vec_t scalar, const TVector4 &v)
|
|
{
|
|
return TVector4(v.X + scalar, v.Y + scalar, v.Z + scalar, v.W + scalar);
|
|
}
|
|
|
|
// Scalar subtraction
|
|
TVector4 &operator-= (vec_t scalar)
|
|
{
|
|
X -= scalar, Y -= scalar, Z -= scalar, W -= scalar;
|
|
return *this;
|
|
}
|
|
|
|
TVector4 operator- (vec_t scalar) const
|
|
{
|
|
return TVector4(X - scalar, Y - scalar, Z - scalar, W - scalar);
|
|
}
|
|
|
|
// Scalar multiplication
|
|
TVector4 &operator*= (vec_t scalar)
|
|
{
|
|
X = vec_t(X *scalar), Y = vec_t(Y * scalar), Z = vec_t(Z * scalar), W = vec_t(W * scalar);
|
|
return *this;
|
|
}
|
|
|
|
friend TVector4 operator* (const TVector4 &v, vec_t scalar)
|
|
{
|
|
return TVector4(v.X * scalar, v.Y * scalar, v.Z * scalar, v.W * scalar);
|
|
}
|
|
|
|
friend TVector4 operator* (vec_t scalar, const TVector4 &v)
|
|
{
|
|
return TVector4(v.X * scalar, v.Y * scalar, v.Z * scalar, v.W * scalar);
|
|
}
|
|
|
|
// Scalar division
|
|
TVector4 &operator/= (vec_t scalar)
|
|
{
|
|
scalar = 1 / scalar, X = vec_t(X * scalar), Y = vec_t(Y * scalar), Z = vec_t(Z * scalar), W = vec_t(W * scalar);
|
|
return *this;
|
|
}
|
|
|
|
TVector4 operator/ (vec_t scalar) const
|
|
{
|
|
scalar = 1 / scalar;
|
|
return TVector4(X * scalar, Y * scalar, Z * scalar, W * scalar);
|
|
}
|
|
|
|
// Vector addition
|
|
TVector4 &operator+= (const TVector4 &other)
|
|
{
|
|
X += other.X, Y += other.Y, Z += other.Z, W += other.W;
|
|
return *this;
|
|
}
|
|
|
|
TVector4 operator+ (const TVector4 &other) const
|
|
{
|
|
return TVector4(X + other.X, Y + other.Y, Z + other.Z, W + other.W);
|
|
}
|
|
|
|
// Vector subtraction
|
|
TVector4 &operator-= (const TVector4 &other)
|
|
{
|
|
X -= other.X, Y -= other.Y, Z -= other.Z, W -= other.W;
|
|
return *this;
|
|
}
|
|
|
|
TVector4 operator- (const TVector4 &other) const
|
|
{
|
|
return TVector4(X - other.X, Y - other.Y, Z - other.Z, W - other.W);
|
|
}
|
|
|
|
// Add a 3D vector to this 4D vector, leaving W unchanged.
|
|
TVector4 &operator+= (const Vector3 &other)
|
|
{
|
|
X += other.X, Y += other.Y, Z += other.Z;
|
|
return *this;
|
|
}
|
|
|
|
// Subtract a 3D vector from this 4D vector, leaving W unchanged.
|
|
TVector4 &operator-= (const Vector3 &other)
|
|
{
|
|
X -= other.X, Y -= other.Y, Z -= other.Z;
|
|
return *this;
|
|
}
|
|
|
|
// Add a 4D vector and a 3D vector.
|
|
friend TVector4 operator+ (const TVector4 &v4, const Vector3 &v3)
|
|
{
|
|
return TVector4(v4.X + v3.X, v4.Y + v3.Y, v4.Z + v3.Z, v4.W);
|
|
}
|
|
|
|
friend TVector4 operator- (const TVector4 &v4, const Vector3 &v3)
|
|
{
|
|
return TVector4(v4.X - v3.X, v4.Y - v3.Y, v4.Z - v3.Z, v4.W);
|
|
}
|
|
|
|
friend Vector3 operator+ (const Vector3 &v3, const TVector4 &v4)
|
|
{
|
|
return Vector3(v3.X + v4.X, v3.Y + v4.Y, v3.Z + v4.Z);
|
|
}
|
|
|
|
// Subtract a 4D vector and a 3D vector.
|
|
// Discards the W component of the 4D vector and returns a 3D vector.
|
|
friend Vector3 operator- (const TVector3<vec_t> &v3, const TVector4 &v4)
|
|
{
|
|
return Vector3(v3.X - v4.X, v3.Y - v4.Y, v3.Z - v4.Z);
|
|
}
|
|
|
|
// Vector length
|
|
double Length() const
|
|
{
|
|
return g_sqrt(LengthSquared());
|
|
}
|
|
|
|
double LengthSquared() const
|
|
{
|
|
return X*X + Y*Y + Z*Z + W*W;
|
|
}
|
|
|
|
double Sum() const
|
|
{
|
|
return abs(X) + abs(Y) + abs(Z) + abs(W);
|
|
}
|
|
|
|
|
|
// Return a unit vector facing the same direction as this one
|
|
TVector4 Unit() const
|
|
{
|
|
double len = Length();
|
|
if (len != 0) len = 1 / len;
|
|
return *this * (vec_t)len;
|
|
}
|
|
|
|
// Scales this vector into a unit vector
|
|
void MakeUnit()
|
|
{
|
|
double len = Length();
|
|
if (len != 0) len = 1 / len;
|
|
*this *= (vec_t)len;
|
|
}
|
|
|
|
// Resizes this vector to be the specified length (if it is not 0)
|
|
TVector4 &MakeResize(double len)
|
|
{
|
|
double vlen = Length();
|
|
if (vlen != 0.)
|
|
{
|
|
double scale = len / vlen;
|
|
X = vec_t(X * scale);
|
|
Y = vec_t(Y * scale);
|
|
Z = vec_t(Z * scale);
|
|
W = vec_t(W * scale);
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
TVector4 Resized(double len) const
|
|
{
|
|
double vlen = Length();
|
|
if (vlen != 0.)
|
|
{
|
|
double scale = len / vlen;
|
|
return{ vec_t(X * scale), vec_t(Y * scale), vec_t(Z * scale), vec_t(W * scale) };
|
|
}
|
|
else
|
|
{
|
|
return *this;
|
|
}
|
|
}
|
|
|
|
// Dot product
|
|
vec_t operator | (const TVector4 &other) const
|
|
{
|
|
return X*other.X + Y*other.Y + Z*other.Z + W*other.W;
|
|
}
|
|
|
|
vec_t dot(const TVector4 &other) const
|
|
{
|
|
return X*other.X + Y*other.Y + Z*other.Z + W*other.W;
|
|
}
|
|
};
|
|
|
|
template<class vec_t>
|
|
struct TMatrix3x3
|
|
{
|
|
typedef TVector3<vec_t> Vector3;
|
|
|
|
vec_t Cells[3][3];
|
|
|
|
TMatrix3x3() = default;
|
|
TMatrix3x3(const TMatrix3x3 &other) = default;
|
|
TMatrix3x3& operator=(const TMatrix3x3& other) = default;
|
|
|
|
TMatrix3x3(const Vector3 &row1, const Vector3 &row2, const Vector3 &row3)
|
|
{
|
|
(*this)[0] = row1;
|
|
(*this)[1] = row2;
|
|
(*this)[2] = row3;
|
|
}
|
|
|
|
// Construct a rotation matrix about an arbitrary axis.
|
|
// (The axis vector must be normalized.)
|
|
TMatrix3x3(const Vector3 &axis, double radians)
|
|
{
|
|
double c = g_cos(radians), s = g_sin(radians), t = 1 - c;
|
|
/* In comments: A more readable version of the matrix setup.
|
|
This was found in Diana Gruber's article "The Mathematics of the
|
|
3D Rotation Matrix" at <http://www.makegames.com/3drotation/> and is
|
|
attributed to Graphics Gems (Glassner, Academic Press, 1990).
|
|
|
|
Cells[0][0] = t*axis.X*axis.X + c;
|
|
Cells[0][1] = t*axis.X*axis.Y - s*axis.Z;
|
|
Cells[0][2] = t*axis.X*axis.Z + s*axis.Y;
|
|
|
|
Cells[1][0] = t*axis.Y*axis.X + s*axis.Z;
|
|
Cells[1][1] = t*axis.Y*axis.Y + c;
|
|
Cells[1][2] = t*axis.Y*axis.Z - s*axis.X;
|
|
|
|
Cells[2][0] = t*axis.Z*axis.X - s*axis.Y;
|
|
Cells[2][1] = t*axis.Z*axis.Y + s*axis.X;
|
|
Cells[2][2] = t*axis.Z*axis.Z + c;
|
|
|
|
Outside comments: A faster version with only 10 (not 24) multiplies.
|
|
*/
|
|
double sx = s*axis.X, sy = s*axis.Y, sz = s*axis.Z;
|
|
double tx, ty, txx, tyy, u, v;
|
|
|
|
tx = t*axis.X;
|
|
Cells[0][0] = vec_t( (txx=tx*axis.X) + c );
|
|
Cells[0][1] = vec_t( (u=tx*axis.Y) - sz);
|
|
Cells[0][2] = vec_t( (v=tx*axis.Z) + sy);
|
|
|
|
ty = t*axis.Y;
|
|
Cells[1][0] = vec_t( u + sz);
|
|
Cells[1][1] = vec_t( (tyy=ty*axis.Y) + c );
|
|
Cells[1][2] = vec_t( (u=ty*axis.Z) - sx);
|
|
|
|
Cells[2][0] = vec_t( v - sy);
|
|
Cells[2][1] = vec_t( u + sx);
|
|
Cells[2][2] = vec_t( (t-txx-tyy) + c );
|
|
}
|
|
|
|
TMatrix3x3(const Vector3 &axis, double c/*cosine*/, double s/*sine*/)
|
|
{
|
|
double t = 1 - c;
|
|
double sx = s*axis.X, sy = s*axis.Y, sz = s*axis.Z;
|
|
double tx, ty, txx, tyy, u, v;
|
|
|
|
tx = t*axis.X;
|
|
Cells[0][0] = vec_t( (txx=tx*axis.X) + c );
|
|
Cells[0][1] = vec_t( (u=tx*axis.Y) - sz);
|
|
Cells[0][2] = vec_t( (v=tx*axis.Z) + sy);
|
|
|
|
ty = t*axis.Y;
|
|
Cells[1][0] = vec_t( u + sz);
|
|
Cells[1][1] = vec_t( (tyy=ty*axis.Y) + c );
|
|
Cells[1][2] = vec_t( (u=ty*axis.Z) - sx);
|
|
|
|
Cells[2][0] = vec_t( v - sy);
|
|
Cells[2][1] = vec_t( u + sx);
|
|
Cells[2][2] = vec_t( (t-txx-tyy) + c );
|
|
}
|
|
|
|
TMatrix3x3(const Vector3 &axis, TAngle<vec_t> degrees);
|
|
|
|
static TMatrix3x3 Rotate2D(double radians)
|
|
{
|
|
double c = g_cos(radians);
|
|
double s = g_sin(radians);
|
|
TMatrix3x3 ret;
|
|
ret.Cells[0][0] = c; ret.Cells[0][1] = -s; ret.Cells[0][2] = 0;
|
|
ret.Cells[1][0] = s; ret.Cells[1][1] = c; ret.Cells[1][2] = 0;
|
|
ret.Cells[2][0] = 0; ret.Cells[2][1] = 0; ret.Cells[2][2] = 1;
|
|
return ret;
|
|
}
|
|
|
|
static TMatrix3x3 Scale2D(TVector2<vec_t> scaleVec)
|
|
{
|
|
TMatrix3x3 ret;
|
|
ret.Cells[0][0] = scaleVec.X; ret.Cells[0][1] = 0; ret.Cells[0][2] = 0;
|
|
ret.Cells[1][0] = 0; ret.Cells[1][1] = scaleVec.Y; ret.Cells[1][2] = 0;
|
|
ret.Cells[2][0] = 0; ret.Cells[2][1] = 0; ret.Cells[2][2] = 1;
|
|
return ret;
|
|
}
|
|
|
|
static TMatrix3x3 Translate2D(TVector2<vec_t> translateVec)
|
|
{
|
|
TMatrix3x3 ret;
|
|
ret.Cells[0][0] = 1; ret.Cells[0][1] = 0; ret.Cells[0][2] = translateVec.X;
|
|
ret.Cells[1][0] = 0; ret.Cells[1][1] = 1; ret.Cells[1][2] = translateVec.Y;
|
|
ret.Cells[2][0] = 0; ret.Cells[2][1] = 0; ret.Cells[2][2] = 1;
|
|
return ret;
|
|
}
|
|
|
|
void Zero()
|
|
{
|
|
memset (this, 0, sizeof *this);
|
|
}
|
|
|
|
void Identity()
|
|
{
|
|
Cells[0][0] = 1; Cells[0][1] = 0; Cells[0][2] = 0;
|
|
Cells[1][0] = 0; Cells[1][1] = 1; Cells[1][2] = 0;
|
|
Cells[2][0] = 0; Cells[2][1] = 0; Cells[2][2] = 1;
|
|
}
|
|
|
|
Vector3 &operator[] (int index)
|
|
{
|
|
return *((Vector3 *)&Cells[index]);
|
|
}
|
|
|
|
const Vector3 &operator[] (int index) const
|
|
{
|
|
return *((Vector3 *)&Cells[index]);
|
|
}
|
|
|
|
// Multiply a scalar
|
|
TMatrix3x3 &operator*= (double scalar)
|
|
{
|
|
(*this)[0] *= scalar;
|
|
(*this)[1] *= scalar;
|
|
(*this)[2] *= scalar;
|
|
return *this;
|
|
}
|
|
|
|
friend TMatrix3x3 operator* (double s, const TMatrix3x3 &m)
|
|
{
|
|
return TMatrix3x3(m[0]*s, m[1]*s, m[2]*s);
|
|
}
|
|
|
|
TMatrix3x3 operator* (double s) const
|
|
{
|
|
return TMatrix3x3((*this)[0]*s, (*this)[1]*s, (*this)[2]*s);
|
|
}
|
|
|
|
// Divide a scalar
|
|
TMatrix3x3 &operator/= (double scalar)
|
|
{
|
|
return *this *= 1 / scalar;
|
|
}
|
|
|
|
TMatrix3x3 operator/ (double s) const
|
|
{
|
|
return *this * (1 / s);
|
|
}
|
|
|
|
// Add two 3x3 matrices together
|
|
TMatrix3x3 &operator+= (const TMatrix3x3 &o)
|
|
{
|
|
(*this)[0] += o[0];
|
|
(*this)[1] += o[1];
|
|
(*this)[2] += o[2];
|
|
return *this;
|
|
}
|
|
|
|
TMatrix3x3 operator+ (const TMatrix3x3 &o) const
|
|
{
|
|
return TMatrix3x3((*this)[0] + o[0], (*this)[1] + o[1], (*this)[2] + o[2]);
|
|
}
|
|
|
|
// Subtract two 3x3 matrices
|
|
TMatrix3x3 &operator-= (const TMatrix3x3 &o)
|
|
{
|
|
(*this)[0] -= o[0];
|
|
(*this)[1] -= o[1];
|
|
(*this)[2] -= o[2];
|
|
return *this;
|
|
}
|
|
|
|
TMatrix3x3 operator- (const TMatrix3x3 &o) const
|
|
{
|
|
return TMatrix3x3((*this)[0] - o[0], (*this)[1] - o[1], (*this)[2] - o[2]);
|
|
}
|
|
|
|
// Concatenate two 3x3 matrices
|
|
TMatrix3x3 &operator*= (const TMatrix3x3 &o)
|
|
{
|
|
return *this = *this * o;
|
|
}
|
|
|
|
TMatrix3x3 operator* (const TMatrix3x3 &o) const
|
|
{
|
|
return TMatrix3x3(
|
|
Vector3(Cells[0][0]*o[0][0] + Cells[0][1]*o[1][0] + Cells[0][2]*o[2][0],
|
|
Cells[0][0]*o[0][1] + Cells[0][1]*o[1][1] + Cells[0][2]*o[2][1],
|
|
Cells[0][0]*o[0][2] + Cells[0][1]*o[1][2] + Cells[0][2]*o[2][2]),
|
|
Vector3(Cells[1][0]*o[0][0] + Cells[1][1]*o[1][0] + Cells[1][2]*o[2][0],
|
|
Cells[1][0]*o[0][1] + Cells[1][1]*o[1][1] + Cells[1][2]*o[2][1],
|
|
Cells[1][0]*o[0][2] + Cells[1][1]*o[1][2] + Cells[1][2]*o[2][2]),
|
|
Vector3(Cells[2][0]*o[0][0] + Cells[2][1]*o[1][0] + Cells[2][2]*o[2][0],
|
|
Cells[2][0]*o[0][1] + Cells[2][1]*o[1][1] + Cells[2][2]*o[2][1],
|
|
Cells[2][0]*o[0][2] + Cells[2][1]*o[1][2] + Cells[2][2]*o[2][2]));
|
|
}
|
|
|
|
// Multiply a 3D vector by a rotation matrix
|
|
friend Vector3 operator* (const Vector3 &v, const TMatrix3x3 &m)
|
|
{
|
|
return Vector3(m[0] | v, m[1] | v, m[2] | v);
|
|
}
|
|
|
|
friend Vector3 operator* (const TMatrix3x3 &m, const Vector3 &v)
|
|
{
|
|
return Vector3(m[0] | v, m[1] | v, m[2] | v);
|
|
}
|
|
};
|
|
|
|
#define BAM_FACTOR (90. / 0x40000000)
|
|
|
|
template<class vec_t>
|
|
struct TAngle
|
|
{
|
|
vec_t Degrees_;
|
|
|
|
// This is to catch any accidental attempt to assign an angle_t to this type. Any explicit exception will require a type cast.
|
|
TAngle(int) = delete;
|
|
TAngle(unsigned int) = delete;
|
|
TAngle(long) = delete;
|
|
TAngle(unsigned long) = delete;
|
|
TAngle &operator= (int other) = delete;
|
|
TAngle &operator= (unsigned other) = delete;
|
|
TAngle &operator= (long other) = delete;
|
|
TAngle &operator= (unsigned long other) = delete;
|
|
|
|
TAngle() = default;
|
|
|
|
private:
|
|
// Both constructors are needed to avoid unnecessary conversions when assigning to FAngle.
|
|
constexpr TAngle (float amt)
|
|
: Degrees_((vec_t)amt)
|
|
{
|
|
}
|
|
constexpr TAngle (double amt)
|
|
: Degrees_((vec_t)amt)
|
|
{
|
|
}
|
|
public:
|
|
|
|
vec_t& Degrees__() { return Degrees_; }
|
|
|
|
static constexpr TAngle fromDeg(float deg)
|
|
{
|
|
return TAngle(deg);
|
|
}
|
|
static constexpr TAngle fromDeg(double deg)
|
|
{
|
|
return TAngle(deg);
|
|
}
|
|
static constexpr TAngle fromDeg(int deg)
|
|
{
|
|
return TAngle((vec_t)deg);
|
|
}
|
|
static constexpr TAngle fromDeg(unsigned deg)
|
|
{
|
|
return TAngle((vec_t)deg);
|
|
}
|
|
|
|
static constexpr TAngle fromRad(float rad)
|
|
{
|
|
return TAngle(float(rad * (180.0f / pi::pif())));
|
|
}
|
|
static constexpr TAngle fromRad(double rad)
|
|
{
|
|
return TAngle(double(rad * (180.0 / pi::pi())));
|
|
}
|
|
|
|
static constexpr TAngle fromBam(int f)
|
|
{
|
|
return TAngle(f * (90. / 0x40000000));
|
|
}
|
|
static constexpr TAngle fromBam(unsigned f)
|
|
{
|
|
return TAngle(f * (90. / 0x40000000));
|
|
}
|
|
|
|
static constexpr TAngle fromBuild(double bang)
|
|
{
|
|
return TAngle(bang * (90. / 512));
|
|
}
|
|
|
|
static constexpr TAngle fromQ16(int bang)
|
|
{
|
|
return TAngle(bang * (90. / 16384));
|
|
}
|
|
|
|
TAngle(const TAngle &other) = default;
|
|
TAngle &operator= (const TAngle &other) = default;
|
|
|
|
constexpr TAngle operator- () const
|
|
{
|
|
return TAngle(-Degrees_);
|
|
}
|
|
|
|
constexpr TAngle &operator+= (TAngle other)
|
|
{
|
|
Degrees_ += other.Degrees_;
|
|
return *this;
|
|
}
|
|
|
|
constexpr TAngle &operator-= (TAngle other)
|
|
{
|
|
Degrees_ -= other.Degrees_;
|
|
return *this;
|
|
}
|
|
|
|
constexpr TAngle operator+ (TAngle other) const
|
|
{
|
|
return Degrees_ + other.Degrees_;
|
|
}
|
|
|
|
constexpr TAngle operator- (TAngle other) const
|
|
{
|
|
return Degrees_ - other.Degrees_;
|
|
}
|
|
|
|
constexpr TAngle &operator*= (vec_t other)
|
|
{
|
|
Degrees_ = Degrees_ * other;
|
|
return *this;
|
|
}
|
|
|
|
constexpr TAngle &operator/= (vec_t other)
|
|
{
|
|
Degrees_ = Degrees_ / other;
|
|
return *this;
|
|
}
|
|
|
|
constexpr TAngle operator* (vec_t other) const
|
|
{
|
|
return Degrees_ * other;
|
|
}
|
|
|
|
constexpr TAngle operator* (TAngle other) const
|
|
{
|
|
return Degrees_ * other.Degrees_;
|
|
}
|
|
|
|
constexpr TAngle operator/ (vec_t other) const
|
|
{
|
|
return Degrees_ / other;
|
|
}
|
|
|
|
constexpr double operator/ (TAngle other) const
|
|
{
|
|
return Degrees_ / other.Degrees_;
|
|
}
|
|
|
|
// Should the comparisons consider an epsilon value?
|
|
constexpr bool operator< (TAngle other) const
|
|
{
|
|
return Degrees_ < other.Degrees_;
|
|
}
|
|
|
|
constexpr bool operator> (TAngle other) const
|
|
{
|
|
return Degrees_ > other.Degrees_;
|
|
}
|
|
|
|
constexpr bool operator<= (TAngle other) const
|
|
{
|
|
return Degrees_ <= other.Degrees_;
|
|
}
|
|
|
|
constexpr bool operator>= (TAngle other) const
|
|
{
|
|
return Degrees_ >= other.Degrees_;
|
|
}
|
|
|
|
constexpr bool operator== (TAngle other) const
|
|
{
|
|
return Degrees_ == other.Degrees_;
|
|
}
|
|
|
|
constexpr bool operator!= (TAngle other) const
|
|
{
|
|
return Degrees_ != other.Degrees_;
|
|
}
|
|
|
|
// Ensure the angle is between [0.0,360.0) degrees
|
|
TAngle Normalized360() const
|
|
{
|
|
// Normalizing the angle converts it to a BAM, which masks it, and converts it back to a float.
|
|
// Note: We MUST use xs_Float here because it is the only method that guarantees reliable wraparound.
|
|
return (vec_t)(BAM_FACTOR * BAMs());
|
|
}
|
|
|
|
// Ensures the angle is between (-180.0,180.0] degrees
|
|
TAngle Normalized180() const
|
|
{
|
|
return (vec_t)(BAM_FACTOR * (signed int)BAMs());
|
|
}
|
|
|
|
constexpr vec_t Radians() const
|
|
{
|
|
return vec_t(Degrees_ * (pi::pi() / 180.0));
|
|
}
|
|
|
|
unsigned BAMs() const
|
|
{
|
|
return xs_CRoundToInt(Degrees_ * (0x40000000 / 90.));
|
|
}
|
|
|
|
constexpr vec_t Degrees() const
|
|
{
|
|
return Degrees_;
|
|
}
|
|
|
|
constexpr int Buildang() const
|
|
{
|
|
return int(Degrees_ * (512 / 90.0));
|
|
}
|
|
|
|
constexpr int Q16() const
|
|
{
|
|
return int(Degrees_ * (16384 / 90.0));
|
|
}
|
|
|
|
TVector2<vec_t> ToVector(vec_t length = 1) const
|
|
{
|
|
return TVector2<vec_t>(length * Cos(), length * Sin());
|
|
}
|
|
|
|
vec_t Cos() const
|
|
{
|
|
return vec_t(g_cosdeg(Degrees_));
|
|
}
|
|
|
|
vec_t Sin() const
|
|
{
|
|
return vec_t(g_sindeg(Degrees_));
|
|
}
|
|
|
|
double Tan() const
|
|
{
|
|
const auto bam = BAMs();
|
|
return g_sinbam(bam) / g_cosbam(bam);
|
|
}
|
|
|
|
// This is for calculating vertical velocity. For high pitches the tangent will become too large to be useful.
|
|
double TanClamped(double max = 5.) const
|
|
{
|
|
return clamp(Tan(), -max, max);
|
|
}
|
|
|
|
int Sgn() const
|
|
{
|
|
return ::Sgn(int(BAMs()));
|
|
}
|
|
};
|
|
|
|
template<class T>
|
|
inline TAngle<T> fabs (const TAngle<T> °)
|
|
{
|
|
return TAngle<T>::fromDeg(fabs(deg.Degrees()));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> abs (const TAngle<T> °)
|
|
{
|
|
return TAngle<T>::fromDeg(fabs(deg.Degrees()));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> deltaangle(const TAngle<T> &a1, const TAngle<T> &a2)
|
|
{
|
|
return (a2 - a1).Normalized180();
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> absangle(const TAngle<T> &a1, const TAngle<T> &a2)
|
|
{
|
|
return fabs(deltaangle(a2, a1));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> clamp(const TAngle<T> &angle, const TAngle<T> &min, const TAngle<T> &max)
|
|
{
|
|
return TAngle<T>::fromDeg(clamp(angle.Degrees(), min.Degrees(), max.Degrees()));
|
|
}
|
|
|
|
inline TAngle<double> VecToAngle(double x, double y)
|
|
{
|
|
return TAngle<double>::fromRad(g_atan2(y, x));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> VecToAngle (const TVector2<T> &vec)
|
|
{
|
|
return TAngle<T>::fromRad(g_atan2(vec.Y, vec.X));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> VecToAngle (const TVector3<T> &vec)
|
|
{
|
|
return TAngle<T>::fromRad(g_atan2(vec.Y, vec.X));
|
|
}
|
|
|
|
template<class T>
|
|
TAngle<T> TVector2<T>::Angle() const
|
|
{
|
|
return VecToAngle(X, Y);
|
|
}
|
|
|
|
template<class T>
|
|
TAngle<T> TVector3<T>::Angle() const
|
|
{
|
|
return VecToAngle(X, Y);
|
|
}
|
|
|
|
template<class T>
|
|
TAngle<T> TVector3<T>::Pitch() const
|
|
{
|
|
return -VecToAngle(XY().Length(), Z);
|
|
}
|
|
|
|
template<class T>
|
|
inline TVector2<T> clamp(const TVector2<T> &vec, const TVector2<T> &min, const TVector2<T> &max)
|
|
{
|
|
return TVector2<T>(clamp(vec.X, min.X, max.X), clamp(vec.Y, min.Y, max.Y));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> interpolatedvalue(const TAngle<T> &oang, const TAngle<T> &ang, const double interpfrac)
|
|
{
|
|
return oang + (deltaangle(oang, ang) * interpfrac);
|
|
}
|
|
|
|
template<class T>
|
|
inline TRotator<T> interpolatedvalue(const TRotator<T> &oang, const TRotator<T> &ang, const double interpfrac)
|
|
{
|
|
return TRotator<T>(
|
|
interpolatedvalue(oang.Pitch, ang.Pitch, interpfrac),
|
|
interpolatedvalue(oang.Yaw, ang.Yaw, interpfrac),
|
|
interpolatedvalue(oang.Roll, ang.Roll, interpfrac)
|
|
);
|
|
}
|
|
|
|
template <class T>
|
|
inline T interpolatedvalue(const T& oval, const T& val, const double interpfrac)
|
|
{
|
|
return T(oval + (val - oval) * interpfrac);
|
|
}
|
|
|
|
// Much of this is copied from TVector3. Is all that functionality really appropriate?
|
|
template<class vec_t>
|
|
struct TRotator
|
|
{
|
|
typedef TAngle<vec_t> Angle;
|
|
|
|
Angle Pitch; // up/down
|
|
Angle Yaw; // left/right
|
|
Angle Roll; // rotation about the forward axis.
|
|
|
|
TRotator() = default;
|
|
|
|
TRotator (const Angle &p, const Angle &y, const Angle &r)
|
|
: Pitch(p), Yaw(y), Roll(r)
|
|
{
|
|
}
|
|
|
|
TRotator(const TRotator &other) = default;
|
|
TRotator &operator= (const TRotator &other) = default;
|
|
|
|
// Access angles as an array
|
|
Angle &operator[] (int index)
|
|
{
|
|
return *(&Pitch + index);
|
|
}
|
|
|
|
const Angle &operator[] (int index) const
|
|
{
|
|
return *(&Pitch + index);
|
|
}
|
|
|
|
// Test for equality
|
|
bool operator== (const TRotator &other) const
|
|
{
|
|
return fabs(Pitch - other.Pitch) < Angle(EQUAL_EPSILON) && fabs(Yaw - other.Yaw) < Angle(EQUAL_EPSILON) && fabs(Roll - other.Roll) < Angle(EQUAL_EPSILON);
|
|
}
|
|
|
|
// Test for inequality
|
|
bool operator!= (const TRotator &other) const
|
|
{
|
|
return fabs(Pitch - other.Pitch) >= Angle(EQUAL_EPSILON) && fabs(Yaw - other.Yaw) >= Angle(EQUAL_EPSILON) && fabs(Roll - other.Roll) >= Angle(EQUAL_EPSILON);
|
|
}
|
|
|
|
// Unary negation
|
|
TRotator operator- () const
|
|
{
|
|
return TRotator(-Pitch, -Yaw, -Roll);
|
|
}
|
|
|
|
// Scalar addition
|
|
TRotator &operator+= (const Angle &scalar)
|
|
{
|
|
Pitch += scalar, Yaw += scalar, Roll += scalar;
|
|
return *this;
|
|
}
|
|
|
|
friend TRotator operator+ (const TRotator &v, const Angle &scalar)
|
|
{
|
|
return TRotator(v.Pitch + scalar, v.Yaw + scalar, v.Roll + scalar);
|
|
}
|
|
|
|
friend TRotator operator+ (const Angle &scalar, const TRotator &v)
|
|
{
|
|
return TRotator(v.Pitch + scalar, v.Yaw + scalar, v.Roll + scalar);
|
|
}
|
|
|
|
// Scalar subtraction
|
|
TRotator &operator-= (const Angle &scalar)
|
|
{
|
|
Pitch -= scalar, Yaw -= scalar, Roll -= scalar;
|
|
return *this;
|
|
}
|
|
|
|
TRotator operator- (const Angle &scalar) const
|
|
{
|
|
return TRotator(Pitch - scalar, Yaw - scalar, Roll - scalar);
|
|
}
|
|
|
|
// Scalar multiplication
|
|
TRotator &operator*= (const Angle &scalar)
|
|
{
|
|
Pitch *= scalar, Yaw *= scalar, Roll *= scalar;
|
|
return *this;
|
|
}
|
|
|
|
friend TRotator operator* (const TRotator &v, const Angle &scalar)
|
|
{
|
|
return TRotator(v.Pitch * scalar, v.Yaw * scalar, v.Roll * scalar);
|
|
}
|
|
|
|
friend TRotator operator* (const Angle &scalar, const TRotator &v)
|
|
{
|
|
return TRotator(v.Pitch * scalar, v.Yaw * scalar, v.Roll * scalar);
|
|
}
|
|
|
|
// Scalar division
|
|
TRotator &operator/= (const Angle &scalar)
|
|
{
|
|
Angle mul(1 / scalar.Degrees_);
|
|
Pitch *= mul, Yaw *= mul, Roll *= mul;
|
|
return *this;
|
|
}
|
|
|
|
TRotator operator/ (const Angle &scalar) const
|
|
{
|
|
Angle mul(1 / scalar.Degrees_);
|
|
return TRotator(Pitch * mul, Yaw * mul, Roll * mul);
|
|
}
|
|
|
|
// Vector addition
|
|
TRotator &operator+= (const TRotator &other)
|
|
{
|
|
Pitch += other.Pitch, Yaw += other.Yaw, Roll += other.Roll;
|
|
return *this;
|
|
}
|
|
|
|
TRotator operator+ (const TRotator &other) const
|
|
{
|
|
return TRotator(Pitch + other.Pitch, Yaw + other.Yaw, Roll + other.Roll);
|
|
}
|
|
|
|
// Vector subtraction
|
|
TRotator &operator-= (const TRotator &other)
|
|
{
|
|
Pitch -= other.Pitch, Yaw -= other.Yaw, Roll -= other.Roll;
|
|
return *this;
|
|
}
|
|
|
|
TRotator operator- (const TRotator &other) const
|
|
{
|
|
return TRotator(Pitch - other.Pitch, Yaw - other.Yaw, Roll - other.Roll);
|
|
}
|
|
};
|
|
|
|
// Create a forward vector from a rotation (ignoring roll)
|
|
template<class T>
|
|
inline TVector3<T>::TVector3 (const TRotator<T> &rot)
|
|
{
|
|
XY() = rot.Pitch.Cos() * rot.Yaw.ToVector();
|
|
Z = rot.Pitch.Sin();
|
|
}
|
|
|
|
template<class T>
|
|
inline TMatrix3x3<T>::TMatrix3x3(const TVector3<T> &axis, TAngle<T> degrees)
|
|
{
|
|
double c = degrees.Cos(), s = degrees.Sin(), t = 1 - c;
|
|
double sx = s*axis.X, sy = s*axis.Y, sz = s*axis.Z;
|
|
double tx, ty, txx, tyy, u, v;
|
|
|
|
tx = t*axis.X;
|
|
Cells[0][0] = T( (txx=tx*axis.X) + c );
|
|
Cells[0][1] = T( (u=tx*axis.Y) - sz );
|
|
Cells[0][2] = T( (v=tx*axis.Z) + sy );
|
|
|
|
ty = t*axis.Y;
|
|
Cells[1][0] = T( u + sz );
|
|
Cells[1][1] = T( (tyy=ty*axis.Y) + c );
|
|
Cells[1][2] = T( (u=ty*axis.Z) - sx );
|
|
|
|
Cells[2][0] = T( v - sy );
|
|
Cells[2][1] = T( u + sx );
|
|
Cells[2][2] = T( (t-txx-tyy) + c );
|
|
}
|
|
|
|
typedef TVector2<float> FVector2;
|
|
typedef TVector3<float> FVector3;
|
|
typedef TVector4<float> FVector4;
|
|
typedef TRotator<float> FRotator;
|
|
typedef TMatrix3x3<float> FMatrix3x3;
|
|
typedef TAngle<float> FAngle;
|
|
|
|
typedef TVector2<double> DVector2;
|
|
typedef TVector3<double> DVector3;
|
|
typedef TVector4<double> DVector4;
|
|
typedef TRotator<double> DRotator;
|
|
typedef TMatrix3x3<double> DMatrix3x3;
|
|
typedef TAngle<double> DAngle;
|
|
|
|
constexpr DAngle nullAngle = DAngle::fromDeg(0.);
|
|
constexpr DAngle minAngle = DAngle::fromDeg(1. / 65536.);
|
|
constexpr FAngle nullFAngle = FAngle::fromDeg(0.);
|
|
|
|
constexpr DAngle DAngle1 = DAngle::fromDeg(1);
|
|
constexpr DAngle DAngle15 = DAngle::fromDeg(15);
|
|
constexpr DAngle DAngle22_5 = DAngle::fromDeg(22.5);
|
|
constexpr DAngle DAngle45 = DAngle::fromDeg(45);
|
|
constexpr DAngle DAngle60 = DAngle::fromDeg(60);
|
|
constexpr DAngle DAngle90 = DAngle::fromDeg(90);
|
|
constexpr DAngle DAngle180 = DAngle::fromDeg(180);
|
|
constexpr DAngle DAngle270 = DAngle::fromDeg(270);
|
|
constexpr DAngle DAngle360 = DAngle::fromDeg(360);
|
|
|
|
class Plane
|
|
{
|
|
public:
|
|
void Set(FVector3 normal, float d)
|
|
{
|
|
m_normal = normal;
|
|
m_d = d;
|
|
}
|
|
|
|
void Init(const FVector3& p1, const FVector3& p2, const FVector3& p3)
|
|
{
|
|
m_normal = ((p2 - p1) ^ (p3 - p1)).Unit();
|
|
m_d = -(p3 |m_normal);
|
|
}
|
|
|
|
// same for a play-vector. Note that y and z are inversed.
|
|
void Set(DVector3 normal, double d)
|
|
{
|
|
m_normal = { (float)normal.X, (float)normal.Z, (float)normal.Y };
|
|
m_d = (float)d;
|
|
}
|
|
|
|
float DistToPoint(float x, float y, float z)
|
|
{
|
|
FVector3 p(x, y, z);
|
|
|
|
return (m_normal | p) + m_d;
|
|
}
|
|
|
|
|
|
bool PointOnSide(float x, float y, float z)
|
|
{
|
|
return DistToPoint(x, y, z) < 0.f;
|
|
}
|
|
|
|
bool PointOnSide(const FVector3 &v) { return PointOnSide(v.X, v.Y, v.Z); }
|
|
|
|
float A() { return m_normal.X; }
|
|
float B() { return m_normal.Y; }
|
|
float C() { return m_normal.Z; }
|
|
float D() { return m_d; }
|
|
|
|
const FVector3 &Normal() const { return m_normal; }
|
|
protected:
|
|
FVector3 m_normal;
|
|
float m_d;
|
|
};
|
|
|
|
#endif
|