mirror of
https://github.com/ZDoom/qzdoom-gpl.git
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1361 lines
29 KiB
C++
1361 lines
29 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 <math.h>
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#include <string.h>
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#include "m_fixed.h"
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#include "tables.h"
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#include "math/cmath.h"
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#define EQUAL_EPSILON (1/65536.f)
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//#define DEG2RAD(d) ((d)*M_PI/180.)
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//#define RAD2DEG(r) ((r)*180./M_PI)
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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 ()
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{
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}
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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)
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: X(other.X), Y(other.Y)
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{
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}
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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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void Zero()
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{
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Y = X = 0;
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}
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TVector2 &operator= (const TVector2 &other)
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{
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// This might seem backwards, but this helps produce smaller code when a newly
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// created vector is assigned, because the components can just be popped off
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// the FPU stack in order without the need for fxch. For platforms with a
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// more sensible registered-based FPU, of course, the order doesn't matter.
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// (And, yes, I know fxch can improve performance in the right circumstances,
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// but this isn't one of those times. Here, it's little more than a no-op that
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// makes the exe 2 bytes larger whenever you assign one vector to another.)
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Y = other.Y, X = other.X;
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return *this;
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}
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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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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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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 (X*X + Y*Y);
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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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// 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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// Dot product
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double 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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// 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)
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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)
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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 vector rotated 90 degrees clockwise.
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TVector2 Rotated90CW()
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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()
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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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vec_t X, Y, Z;
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TVector3 ()
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{
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}
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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 (const TVector3 &other)
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: X(other.X), Y(other.Y), Z(other.Z)
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{
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}
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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 &operator= (const TVector3 &other)
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{
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Z = other.Z, Y = other.Y, X = other.X;
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return *this;
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}
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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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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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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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Vector2 XY() const
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{
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return{ X, Y };
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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 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 TVector3 &v3, const Vector2 &v2)
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{
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return Vector2(v3.X - v2.X, v3.Y - v2.Y);
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}
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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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|
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// Returns the angle (in radians) that the ray (0,0)-(X,Y) faces
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TAngle<vec_t> Angle() const;
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TAngle<vec_t> Pitch() const;
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// Vector length
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double Length() const
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{
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return g_sqrt (X*X + Y*Y + Z*Z);
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}
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double LengthSquared() const
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{
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return X*X + Y*Y + Z*Z;
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}
|
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// Return a unit vector facing the same direction as this one
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TVector3 Unit() const
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{
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double 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
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|
void MakeUnit()
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{
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double len = Length();
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if (len != 0) len = 1 / len;
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*this *= 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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TVector3 &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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Z = vec_t(Z * scale);
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return *this;
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}
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TVector3 Resized(double len)
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{
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double scale = len / Length();
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return{ vec_t(X * scale), vec_t(Y * scale), vec_t(Z * scale) };
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}
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// Dot product
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double 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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|
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// Cross product
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|
TVector3 operator ^ (const TVector3 &other) const
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|
{
|
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return TVector3(Y*other.Z - Z*other.Y,
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Z*other.X - X*other.Z,
|
|
X*other.Y - Y*other.X);
|
|
}
|
|
|
|
TVector3 &operator ^= (const TVector3 &other)
|
|
{
|
|
*this = *this ^ other;
|
|
}
|
|
};
|
|
|
|
template<class vec_t>
|
|
struct TMatrix3x3
|
|
{
|
|
typedef TVector3<vec_t> Vector3;
|
|
|
|
vec_t Cells[3][3];
|
|
|
|
TMatrix3x3()
|
|
{
|
|
}
|
|
|
|
TMatrix3x3(const TMatrix3x3 &other)
|
|
{
|
|
(*this)[0] = other[0];
|
|
(*this)[1] = other[1];
|
|
(*this)[2] = other[2];
|
|
}
|
|
|
|
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);
|
|
|
|
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);
|
|
}
|
|
};
|
|
|
|
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 ()
|
|
{
|
|
}
|
|
|
|
TAngle (vec_t amt)
|
|
: Degrees(amt)
|
|
{
|
|
}
|
|
|
|
/*
|
|
TAngle (int amt)
|
|
: Degrees(vec_t(amt))
|
|
{
|
|
}
|
|
*/
|
|
|
|
TAngle (const TAngle &other)
|
|
: Degrees(other.Degrees)
|
|
{
|
|
}
|
|
|
|
TAngle &operator= (const TAngle &other)
|
|
{
|
|
Degrees = other.Degrees;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator= (double other)
|
|
{
|
|
Degrees = other;
|
|
return *this;
|
|
}
|
|
|
|
// intentionally disabled so that common math functions cannot be accidentally called with a TAngle.
|
|
//operator vec_t() const { return Degrees; }
|
|
|
|
TAngle operator- () const
|
|
{
|
|
return TAngle(-Degrees);
|
|
}
|
|
|
|
TAngle &operator+= (TAngle other)
|
|
{
|
|
Degrees += other.Degrees;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator-= (TAngle other)
|
|
{
|
|
Degrees -= other.Degrees;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator*= (TAngle other)
|
|
{
|
|
Degrees *= other.Degrees;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator/= (TAngle other)
|
|
{
|
|
Degrees /= other.Degrees;
|
|
return *this;
|
|
}
|
|
|
|
TAngle operator+ (TAngle other) const
|
|
{
|
|
return Degrees + other.Degrees;
|
|
}
|
|
|
|
TAngle operator- (TAngle other) const
|
|
{
|
|
return Degrees - other.Degrees;
|
|
}
|
|
|
|
TAngle operator* (TAngle other) const
|
|
{
|
|
return Degrees * other.Degrees;
|
|
}
|
|
|
|
TAngle operator/ (TAngle other) const
|
|
{
|
|
return Degrees / other.Degrees;
|
|
}
|
|
|
|
TAngle &operator+= (vec_t other)
|
|
{
|
|
Degrees = Degrees + other;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator-= (vec_t other)
|
|
{
|
|
Degrees = Degrees - other;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator*= (vec_t other)
|
|
{
|
|
Degrees = Degrees * other;
|
|
return *this;
|
|
}
|
|
|
|
TAngle &operator/= (vec_t other)
|
|
{
|
|
Degrees = Degrees / other;
|
|
return *this;
|
|
}
|
|
|
|
TAngle operator+ (vec_t other) const
|
|
{
|
|
return Degrees + other;
|
|
}
|
|
|
|
TAngle operator- (vec_t other) const
|
|
{
|
|
return Degrees - other;
|
|
}
|
|
|
|
friend TAngle operator- (vec_t o1, TAngle o2)
|
|
{
|
|
return TAngle(o1 - o2.Degrees);
|
|
}
|
|
|
|
TAngle operator* (vec_t other) const
|
|
{
|
|
return Degrees * other;
|
|
}
|
|
|
|
TAngle operator/ (vec_t other) const
|
|
{
|
|
return Degrees / other;
|
|
}
|
|
|
|
// Should the comparisons consider an epsilon value?
|
|
bool operator< (TAngle other) const
|
|
{
|
|
return Degrees < other.Degrees;
|
|
}
|
|
|
|
bool operator> (TAngle other) const
|
|
{
|
|
return Degrees > other.Degrees;
|
|
}
|
|
|
|
bool operator<= (TAngle other) const
|
|
{
|
|
return Degrees <= other.Degrees;
|
|
}
|
|
|
|
bool operator>= (TAngle other) const
|
|
{
|
|
return Degrees >= other.Degrees;
|
|
}
|
|
|
|
bool operator== (TAngle other) const
|
|
{
|
|
return Degrees == other.Degrees;
|
|
}
|
|
|
|
bool operator!= (TAngle other) const
|
|
{
|
|
return Degrees != other.Degrees;
|
|
}
|
|
|
|
bool operator< (vec_t other) const
|
|
{
|
|
return Degrees < other;
|
|
}
|
|
|
|
bool operator> (vec_t other) const
|
|
{
|
|
return Degrees > other;
|
|
}
|
|
|
|
bool operator<= (vec_t other) const
|
|
{
|
|
return Degrees <= other;
|
|
}
|
|
|
|
bool operator>= (vec_t other) const
|
|
{
|
|
return Degrees >= other;
|
|
}
|
|
|
|
bool operator== (vec_t other) const
|
|
{
|
|
return Degrees == other;
|
|
}
|
|
|
|
bool operator!= (vec_t other) const
|
|
{
|
|
return Degrees != other;
|
|
}
|
|
|
|
// Ensure the angle is between [0.0,360.0) degrees
|
|
TAngle &Normalize360()
|
|
{
|
|
// 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.
|
|
Degrees = (vec_t)ANGLE2DBL((unsigned int)FLOAT2ANGLE(Degrees));
|
|
return *this;
|
|
}
|
|
|
|
// Ensures the angle is between (-180.0,180.0] degrees
|
|
TAngle &Normalize180()
|
|
{
|
|
Degrees = (vec_t)ANGLE2DBL((signed int)FLOAT2ANGLE(Degrees));
|
|
return *this;
|
|
}
|
|
|
|
// Same as above but doesn't alter the calling object itself
|
|
|
|
// Ensure the angle is between [0.0,360.0) degrees
|
|
TAngle Normalized360() const
|
|
{
|
|
|
|
return (vec_t)ANGLE2DBL((unsigned int)FLOAT2ANGLE(Degrees));
|
|
}
|
|
|
|
// Ensures the angle is between (-180.0,180.0] degrees
|
|
TAngle Normalized180() const
|
|
{
|
|
return (vec_t)ANGLE2DBL((signed int)FLOAT2ANGLE(Degrees));
|
|
}
|
|
|
|
// Like Normalize360(), except the integer value is not converted back to a float.
|
|
// The steps parameter must be a power of 2.
|
|
int Quantize(int steps) const
|
|
{
|
|
return xs_CRoundToInt((Degrees * (steps/360.0)) & (steps-1));
|
|
}
|
|
|
|
vec_t Radians() const
|
|
{
|
|
return Degrees * (M_PI / 180.0);
|
|
}
|
|
|
|
unsigned BAMs() const
|
|
{
|
|
return FLOAT2ANGLE(Degrees);
|
|
}
|
|
|
|
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
|
|
{
|
|
return g_tan(Degrees * (M_PI / 180.));
|
|
}
|
|
|
|
// 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);
|
|
}
|
|
|
|
};
|
|
|
|
template<class T>
|
|
inline double ToRadians (const TAngle<T> °)
|
|
{
|
|
return double(deg.Degrees * (M_PI / 180.0));
|
|
}
|
|
|
|
// If this gets templated there will be countless instantiation errors.
|
|
inline TAngle<double> ToDegrees (double rad)
|
|
{
|
|
return TAngle<double> (double(rad * (180.0 / M_PI)));
|
|
}
|
|
|
|
// Emulates the old floatbob offset table with direct calls to trig functions.
|
|
inline double BobSin(double fb)
|
|
{
|
|
return TAngle<double>(double(fb * (180.0 / 32))).Sin() * 8;
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> fabs (const TAngle<T> °)
|
|
{
|
|
return TAngle<T>(fabs(deg.Degrees));
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> deltaangle(const TAngle<T> &a1, const TAngle<T> &a2)
|
|
{
|
|
return (a2 - a1).Normalize180();
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> deltaangle(const TAngle<T> &a1, double a2)
|
|
{
|
|
return (a2 - a1).Normalize180();
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> deltaangle(double a1, const TAngle<T> &a2)
|
|
{
|
|
return (a2 - a1).Normalize180();
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> absangle(const TAngle<T> &a1, const TAngle<T> &a2)
|
|
{
|
|
return fabs((a1 - a2).Normalize180());
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> absangle(const TAngle<T> &a1, double a2)
|
|
{
|
|
return fabs((a1 - a2).Normalize180());
|
|
}
|
|
|
|
inline TAngle<double> VecToAngle(double x, double y)
|
|
{
|
|
return g_atan2(y, x) * (180.0 / M_PI);
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> VecToAngle (const TVector2<T> &vec)
|
|
{
|
|
return (T)g_atan2(vec.Y, vec.X) * (180.0 / M_PI);
|
|
}
|
|
|
|
template<class T>
|
|
inline TAngle<T> VecToAngle (const TVector3<T> &vec)
|
|
{
|
|
return (T)g_atan2(vec.Y, vec.X) * (180.0 / M_PI);
|
|
}
|
|
|
|
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(TVector2<T>(X, Y).Length(), Z);
|
|
}
|
|
|
|
// 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 ()
|
|
{
|
|
}
|
|
|
|
TRotator (const Angle &p, const Angle &y, const Angle &r)
|
|
: Pitch(p), Yaw(y), Roll(r)
|
|
{
|
|
}
|
|
|
|
TRotator (const TRotator &other)
|
|
: Pitch(other.Pitch), Yaw(other.Yaw), Roll(other.Roll)
|
|
{
|
|
}
|
|
|
|
TRotator &operator= (const TRotator &other)
|
|
{
|
|
Roll = other.Roll, Yaw = other.Yaw, Pitch = other.Pitch;
|
|
return *this;
|
|
}
|
|
|
|
// 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 *= scalar, Yaw *= scalar, Roll *= scalar;
|
|
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);
|
|
}
|
|
|
|
// Normalize each component
|
|
TRotator &Normalize180 ()
|
|
{
|
|
for (int i = -3; i; ++i)
|
|
{
|
|
(*this)[i+3].Normalize180();
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
TRotator &Normalize360 ()
|
|
{
|
|
for (int i = -3; i; ++i)
|
|
{
|
|
(*this)[i+3].Normalize360();
|
|
}
|
|
return *this;
|
|
}
|
|
};
|
|
|
|
// Create a forward vector from a rotation (ignoring roll)
|
|
|
|
template<class T>
|
|
inline TVector3<T>::TVector3 (const TRotator<T> &rot)
|
|
{
|
|
double pcos = rot.Pitch.Cos();
|
|
X = pcos * rot.Yaw.Cos();
|
|
Y = pcos * rot.Yaw.Sin();
|
|
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 TRotator<float> FRotator;
|
|
typedef TMatrix3x3<float> FMatrix3x3;
|
|
typedef TAngle<float> FAngle;
|
|
|
|
typedef TVector2<double> DVector2;
|
|
typedef TVector3<double> DVector3;
|
|
typedef TRotator<double> DRotator;
|
|
typedef TMatrix3x3<double> DMatrix3x3;
|
|
typedef TAngle<double> DAngle;
|
|
|
|
#endif
|