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1024 lines
36 KiB
C
1024 lines
36 KiB
C
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/*
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===========================================================================
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Copyright (C) 2000 - 2013, Raven Software, Inc.
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Copyright (C) 2001 - 2013, Activision, Inc.
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Copyright (C) 2013 - 2015, OpenJK contributors
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This file is part of the OpenJK source code.
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OpenJK is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License version 2 as
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published by the Free Software Foundation.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, see <http://www.gnu.org/licenses/>.
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===========================================================================
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*/
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////////////////////////////////////////////////////////////////////////////////////////
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// RAVEN STANDARD TEMPLATE LIBRARY
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// (c) 2002 Activision
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//
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//
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// Vector Library
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// --------------
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// The base implimention of the Raven Vector object attempts to solve a number of
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// high level problems as efficiently as possible. Where ever feasible, functions have
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// been included in the .h file so the compiler can inline them.
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//
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// The vectors define the following operations:
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// - Construction
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// - Initialization
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// - Member Access
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// - Equality / Inequality Operators
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// - Arithimitic Operators
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// - Length & Distance
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// - Normalization (Standard, Safe, Angular)
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// - Dot & Cross Product
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// - Perpendicular Vector
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// - Truncation
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// - Min & Max Element Analisis
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// - Interpolation
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// - Angle / Vector Conversion
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// - Translation & Rotation
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// - Point and Line Intersection Tests
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// - Left / Right Line Test
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// - String Operations
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// - Debug Routines
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// - "Standard" Vectors As Static Memebers
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//
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// As necessary, some projects may #define special faster versions of these routines to
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// make better use of native hardware / software implimentations.
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//
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//
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//
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//
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// NOTES:
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// 05/29/02 - CREATED
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// 05/30/02 - RotatePoint() is currently unimplimented. Waiting for Matrix Library
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//
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//
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////////////////////////////////////////////////////////////////////////////////////////
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#if !defined(RAVL_VEC_INC)
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#define RAVL_VEC_INC
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//namespace ravl
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//{
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template <class T> T Min(const T& a, const T& b) {return (a<b)?(a):(b);}
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template <class T> T Max(const T& a, const T& b) {return (b<a)?(a):(b);}
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////////////////////////////////////////////////////////////////////////////////////////
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// Defines
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////////////////////////////////////////////////////////////////////////////////////////
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#define RAVL_VEC_UDF (1.234567E-10f) // Undefined Vector Value (for debugging)
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#define RAVL_VEC_PI (3.1415926535f) // Pi
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#define RAVL_VEC_DEGTORADCONST (0.0174532925f) // (RAVL_VEC_PI / 180.0f)
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#define RAVL_VEC_RADTODEGCONST (57.295779514f) // (180.0f / RAVL_VEC_PI)
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#define RAVL_VEC_DEGTORAD( a ) ( (a) * RAVL_VEC_DEGTORADCONST ) // Quick Macro For Degrees -> Radians
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#define RAVL_VEC_RADTODEG( a ) ( (a) * RAVL_VEC_RADTODEGCONST ) // Quick Macro For Radians -> Degrees
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////////////////////////////////////////////////////////////////////////////////////////
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// Enums And Typedefs
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////////////////////////////////////////////////////////////////////////////////////////
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enum ESide
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{
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Side_None = 0,
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Side_Left = 1,
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Side_Right = 2,
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Side_In = 3,
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Side_Out = 4,
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Side_AllIn = 5
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};
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////////////////////////////////////////////////////////////////////////////////////////
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// The 4 Dimensional Vector
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////////////////////////////////////////////////////////////////////////////////////////
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class CVec4
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{
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public:
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////////////////////////////////////////////////////////////////////////////////////
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// Constructors
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////////////////////////////////////////////////////////////////////////////////////
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#ifndef _DEBUG
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CVec4() {}
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#else
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CVec4() {v[0]=v[1]=v[2]=v[3]=RAVL_VEC_UDF;} // DEBUG INITIALIZATION
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#endif
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CVec4(const float val) {v[0]=val; v[1]=val; v[2]=val; v[3]=val;}
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CVec4(const float x,const float y,const float z, const float r) {v[0]=x; v[1]=y; v[2]=z; v[3]=r;}
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CVec4(const CVec4& t) {v[0]=t.v[0]; v[1]=t.v[1]; v[2]=t.v[2]; v[3]=t.v[3];}
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CVec4(const float *t) {v[0]=t[0]; v[1]=t[1]; v[2]=t[2]; v[3]=t[3];}
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////////////////////////////////////////////////////////////////////////////////////
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// Initializers
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////////////////////////////////////////////////////////////////////////////////////
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void Set(const float t) {v[0]=t; v[1]=t; v[2]=t; v[3]=t;}
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void Set(const float *t) {v[0]=t[0]; v[1]=t[1]; v[2]=t[2]; v[3]=t[3];}
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void Set(const float x,const float y,const float z, const float r) {v[0]=x; v[1]=y; v[2]=z; v[3]=r;}
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void Clear() {v[0]=0; v[1]=0; v[2]=0; v[3]=0;}
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////////////////////////////////////////////////////////////////////////////////////
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// Member Accessors
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////////////////////////////////////////////////////////////////////////////////////
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const float& operator[](int i) const {return v[i];}
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float& operator[](int i) {return v[i];}
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float& pitch() {return v[0];}
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float& yaw() {return v[1];}
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float& roll() {return v[2];}
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float& radius() {return v[3];}
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////////////////////////////////////////////////////////////////////////////////////
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// Equality / Inequality Operators
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////////////////////////////////////////////////////////////////////////////////////
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bool operator! () const {return !(v[0] && v[1] && v[2] && v[3] );}
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bool operator== (const CVec4& t) const {return (v[0]==t.v[0] && v[1]==t.v[1] && v[2]==t.v[2] && v[3]==t.v[3]);}
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bool operator!= (const CVec4& t) const {return !(v[0]==t.v[0] && v[1]==t.v[1] && v[2]==t.v[2] && v[3]==t.v[3]);}
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bool operator< (const CVec4& t) const {return (v[0]< t.v[0] && v[1]< t.v[1] && v[2]< t.v[2] && v[3]< t.v[3]);}
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bool operator> (const CVec4& t) const {return (v[0]> t.v[0] && v[1]> t.v[1] && v[2]> t.v[2] && v[3]> t.v[3]);}
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bool operator<= (const CVec4& t) const {return (v[0]<=t.v[0] && v[1]<=t.v[1] && v[2]<=t.v[2] && v[3]<=t.v[3]);}
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bool operator>= (const CVec4& t) const {return (v[0]>=t.v[0] && v[1]>=t.v[1] && v[2]>=t.v[2] && v[3]>=t.v[3]);}
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////////////////////////////////////////////////////////////////////////////////////
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// Basic Arithimitic Operators
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////////////////////////////////////////////////////////////////////////////////////
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const CVec4 &operator= (const float d) {v[0]=d; v[1]=d; v[2]=d; v[3]=d; return *this;}
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const CVec4 &operator= (const CVec4& t) {v[0]=t.v[0]; v[1]=t.v[1]; v[2]=t.v[2]; v[3]=t.v[3]; return *this;}
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const CVec4 &operator+= (const float d) {v[0]+=d; v[1]+=d; v[2]+=d; v[3]+=d; return *this;}
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const CVec4 &operator+= (const CVec4& t) {v[0]+=t.v[0]; v[1]+=t.v[1]; v[2]+=t.v[2]; v[3]+=t.v[3];return *this;}
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const CVec4 &operator-= (const float d) {v[0]-=d; v[1]-=d; v[2]-=d; v[3]-=d; return *this;}
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const CVec4 &operator-= (const CVec4& t) {v[0]-=t.v[0]; v[1]-=t.v[1]; v[2]-=t.v[2]; v[3]-=t.v[3];return *this;}
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const CVec4 &operator*= (const float d) {v[0]*=d; v[1]*=d; v[2]*=d; v[3]*=d; return *this;}
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const CVec4 &operator*= (const CVec4& t) {v[0]*=t.v[0]; v[1]*=t.v[1]; v[2]*=t.v[2]; v[3]*=t.v[3];return *this;}
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const CVec4 &operator/= (const float d) {v[0]/=d; v[1]/=d; v[2]/=d; v[3]/=d; return *this;}
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const CVec4 &operator/= (const CVec4& t) {v[0]/=t.v[0]; v[1]/=t.v[1]; v[2]/=t.v[2]; v[3]/=t.v[3];return *this;}
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inline CVec4 operator+ (const CVec4 &t) const {return CVec4(v[0]+t.v[0], v[1]+t.v[1], v[2]+t.v[2], v[3]+t.v[3]);}
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inline CVec4 operator- (const CVec4 &t) const {return CVec4(v[0]-t.v[0], v[1]-t.v[1], v[2]-t.v[2], v[3]-t.v[3]);}
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inline CVec4 operator* (const CVec4 &t) const {return CVec4(v[0]*t.v[0], v[1]*t.v[1], v[2]*t.v[2], v[3]*t.v[3]);}
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inline CVec4 operator/ (const CVec4 &t) const {return CVec4(v[0]/t.v[0], v[1]/t.v[1], v[2]/t.v[2], v[3]/t.v[3]);}
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////////////////////////////////////////////////////////////////////////////////////
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// Length And Distance Calculations
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////////////////////////////////////////////////////////////////////////////////////
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float Len() const;
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float Len2() const {return (v[0]*v[0]+v[1]*v[1]+v[2]*v[2]+v[3]*v[3]);}
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float Dist(const CVec4& t) const;
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float Dist2(const CVec4& t) const {return ((t.v[0]-v[0])*(t.v[0]-v[0]) + (t.v[1]-v[1])*(t.v[1]-v[1]) + (t.v[2]-v[2])*(t.v[2]-v[2]) + (t.v[3]-v[3])*(t.v[3]-v[3]) );}
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////////////////////////////////////////////////////////////////////////////////////
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// Normalization
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////////////////////////////////////////////////////////////////////////////////////
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float Norm();
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float SafeNorm();
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void AngleNorm();
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////////////////////////////////////////////////////////////////////////////////////
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// Dot, Cross & Perpendicular Vector
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////////////////////////////////////////////////////////////////////////////////////
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float Dot(const CVec4& t) const {return (v[0]*t.v[0] + v[1]*t.v[1] + v[2]*t.v[2] + v[3]*t.v[3]);}
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void Cross(const CVec4& t)
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{
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CVec4 temp(*this);
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v[0] = (temp.v[1]*t.v[2]) - (temp.v[2]*t.v[1]);
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v[1] = (temp.v[2]*t.v[0]) - (temp.v[0]*t.v[2]);
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v[2] = (temp.v[0]*t.v[1]) - (temp.v[1]*t.v[0]);
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v[3] = 0;
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}
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void Perp();
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////////////////////////////////////////////////////////////////////////////////////
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// Truncation & Element Analysis
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////////////////////////////////////////////////////////////////////////////////////
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void Min(const CVec4& t)
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{
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if (t.v[0]<v[0]) v[0]=t.v[0];
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if (t.v[1]<v[1]) v[1]=t.v[1];
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if (t.v[2]<v[2]) v[2]=t.v[2];
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if (t.v[3]<v[3]) v[3]=t.v[3];
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}
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void Max(const CVec4& t)
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{
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if (t.v[0]>v[0]) v[0]=t.v[0];
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if (t.v[1]>v[1]) v[1]=t.v[1];
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if (t.v[2]>v[2]) v[2]=t.v[2];
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if (t.v[3]>v[3]) v[3]=t.v[3];
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}
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float MaxElement() const
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{
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return v[MaxElementIndex()];
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}
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int MaxElementIndex() const;
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////////////////////////////////////////////////////////////////////////////////////
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// Interpolation
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////////////////////////////////////////////////////////////////////////////////////
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void Interp(const CVec4 &v1, const CVec4 &v2, const float t)
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{
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(*this)=v1;
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(*this)-=v2;
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(*this)*=t;
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(*this)+=v2;
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}
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void ScaleAdd(const CVec4& t, const float scale)
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{
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v[0] += (scale * t.v[0]);
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v[1] += (scale * t.v[1]);
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v[2] += (scale * t.v[2]);
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v[3] += (scale * t.v[3]);
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}
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////////////////////////////////////////////////////////////////////////////////////
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// Conversion Angle To Vector (Angle In Degrees)
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////////////////////////////////////////////////////////////////////////////////////
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void VecToAng();
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void AngToVec();
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void AngToVec(CVec4& Right, CVec4& Up);
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////////////////////////////////////////////////////////////////////////////////////
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// Conversion Angle To Vector (Angle In Radians)
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////////////////////////////////////////////////////////////////////////////////////
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void VecToAngRad();
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void AngToVecRad();
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void AngToVecRad(CVec4& Right, CVec4& Up);
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////////////////////////////////////////////////////////////////////////////////////
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// Conversion Between Radians And Degrees
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////////////////////////////////////////////////////////////////////////////////////
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void ToRadians();
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void ToDegrees();
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////////////////////////////////////////////////////////////////////////////////////
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// Project
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//
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// Standard projection function. Take the (this) and project it onto the vector
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// (U). Imagine drawing a line perpendicular to U from the endpoint of the (this)
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// Vector. That then becomes the new vector.
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//
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// The value returned is the scale of the new vector with respect to the one passed
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// to the function. If the scale is less than (1.0) then the new vector is shorter
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// than (U). If the scale is negative, then the vector is going in the opposite
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// direction of (U).
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//
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// _ (U)
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// /|
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// / _ (this)
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// / RESULTS-> /|
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// / /
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// / __\ (this) /
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// /___--- / /
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//
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////////////////////////////////////////////////////////////////////////////////////
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float Project(const CVec4 &U)
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{
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float Scale = (Dot(U) / U.Len2()); // Find the scale of this vector on U
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(*this)=U; // Copy U onto this vector
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(*this)*=Scale; // Use the previously calculated scale to get the right length.
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return Scale;
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}
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////////////////////////////////////////////////////////////////////////////////////
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// Project To Line
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//
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// This function takes two other points in space as the start and end of a line
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// segment and projects the (this) point onto the line defined by (Start)->(Stop)
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//
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// RETURN VALUES:
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// (-INF, 0.0) : (this) landed on the line before (Start)
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// (0.0, 1.0) : (this) landed in the line segment between (Start) and (Stop)
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// (1.0, INF) : (this) landed on the line beyond (End)
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//
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// (Stop)
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// /
|
||
|
|
// /
|
||
|
|
// o _
|
||
|
|
// / |\
|
||
|
|
// / (this)
|
||
|
|
// /
|
||
|
|
// (Start)
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float ProjectToLine(const CVec4 &Start, const CVec4 &Stop)
|
||
|
|
{
|
||
|
|
(*this) -= Start;
|
||
|
|
float Scale = Project(Stop - Start);
|
||
|
|
(*this) += Start;
|
||
|
|
return Scale;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Project To Line Seg
|
||
|
|
//
|
||
|
|
// Same As Project To Line, Except It Will Clamp To Start And Stop
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float ProjectToLineSeg(const CVec4 &Start, const CVec4 &Stop)
|
||
|
|
{
|
||
|
|
float Scale = ProjectToLine(Start, Stop);
|
||
|
|
if (Scale<0.0f)
|
||
|
|
{
|
||
|
|
(*this) = Start;
|
||
|
|
}
|
||
|
|
else if (Scale>1.0f)
|
||
|
|
{
|
||
|
|
(*this) = Stop;
|
||
|
|
}
|
||
|
|
return Scale;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Distance To Line
|
||
|
|
//
|
||
|
|
// Uses project to line and than calculates distance to the new point
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float DistToLine(const CVec4 &Start, const CVec4 &Stop) const
|
||
|
|
{
|
||
|
|
CVec4 P(*this);
|
||
|
|
P.ProjectToLineSeg(Start, Stop);
|
||
|
|
|
||
|
|
return Dist(P);
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Distance To Line
|
||
|
|
//
|
||
|
|
// Uses project to line and than calculates distance to the new point
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float DistToLine2(const CVec4 &Start, const CVec4 &Stop) const
|
||
|
|
{
|
||
|
|
CVec4 P(*this);
|
||
|
|
P.ProjectToLineSeg(Start, Stop);
|
||
|
|
|
||
|
|
return Dist2(P);
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Translation & Rotation (2D)
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void RotatePoint(const CVec4 &Angle, const CVec4 &Origin);
|
||
|
|
void Reposition(const CVec4 &Translation, float RotationDegrees=0.0);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Area Of The Parallel Pipid (2D)
|
||
|
|
//
|
||
|
|
// Given two more points, this function calculates the area of the parallel pipid
|
||
|
|
// formed.
|
||
|
|
//
|
||
|
|
// Note: This function CAN return a negative "area" if (this) is above or right of
|
||
|
|
// (A) and (B)... We do not take the abs because the sign of the "area" is needed
|
||
|
|
// for the left right test (see below)
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// ___---( ... )
|
||
|
|
// (A)---/ /
|
||
|
|
// / /
|
||
|
|
// / /
|
||
|
|
// / /
|
||
|
|
// / ___---(B)
|
||
|
|
// (this)---/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float AreaParallelPipid(const CVec4 &A, const CVec4 &B) const
|
||
|
|
{
|
||
|
|
return ((A.v[0]*B.v[1] - A.v[1]*B.v[0]) +
|
||
|
|
(B.v[0]* v[1] - v[0]*B.v[1]) +
|
||
|
|
( v[0]*A.v[1] - A.v[0]* v[1]));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Area Of The Triangle (2D)
|
||
|
|
//
|
||
|
|
// Given two more points, this function calculates the area of the triangle formed.
|
||
|
|
//
|
||
|
|
// (A)
|
||
|
|
// / \__
|
||
|
|
// / \__
|
||
|
|
// / \_
|
||
|
|
// / ___---(B)
|
||
|
|
// (this)---/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float AreaTriange(const CVec4 &A, const CVec4 &B) const
|
||
|
|
{
|
||
|
|
return (AreaParallelPipid(A, B) * 0.5f);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// The Left Right Test (2D)
|
||
|
|
//
|
||
|
|
// Given a line segment (Start->End) and a tolerance for *right on*, this function
|
||
|
|
// evaluates which side the point is of the line. (Side_Left in this example)
|
||
|
|
//
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// (this) ___---/(End)
|
||
|
|
// ___---/
|
||
|
|
// ___---/
|
||
|
|
// (Start)/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
ESide LRTest(const CVec4 &Start, const CVec4 &End, float Tolerance=0.0) const
|
||
|
|
{
|
||
|
|
float Area = AreaParallelPipid(Start, End);
|
||
|
|
if (Area>Tolerance)
|
||
|
|
{
|
||
|
|
return Side_Left;
|
||
|
|
}
|
||
|
|
if (Area<(Tolerance*-1))
|
||
|
|
{
|
||
|
|
return Side_Right;
|
||
|
|
}
|
||
|
|
return Side_None;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Point In Circumscribed Circle (True/False)
|
||
|
|
//
|
||
|
|
// Returns true if the given point is within the circumscribed
|
||
|
|
// circle of the given ABC Triangle:
|
||
|
|
// _____
|
||
|
|
// / B \
|
||
|
|
// / / \ \
|
||
|
|
// | / \ |
|
||
|
|
// |A---------C|
|
||
|
|
// \ Pt /
|
||
|
|
// \_______/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool PtInCircle(const CVec4 &A, const CVec4 &B, const CVec4 &C) const;
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Point In Standard Circle (True/False)
|
||
|
|
//
|
||
|
|
// Returns true if the given point is within the Circle
|
||
|
|
// _____
|
||
|
|
// / \
|
||
|
|
// / \
|
||
|
|
// | Circle |
|
||
|
|
// | |
|
||
|
|
// \ Pt /
|
||
|
|
// \_______/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool PtInCircle(const CVec4 &Circle, float Radius) const;
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Line Intersects Circle (True/False)
|
||
|
|
//
|
||
|
|
// r - Radius Of The Circle
|
||
|
|
// A - Start Of Line Segment
|
||
|
|
// B - End Of Line Segment
|
||
|
|
//
|
||
|
|
// P - Projected Position Of Origin Onto Line AB
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// (Stop)
|
||
|
|
// /
|
||
|
|
// /
|
||
|
|
// (P)
|
||
|
|
// / \ \
|
||
|
|
// / (this)-r->|
|
||
|
|
// / /
|
||
|
|
// (Start)
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool LineInCircle(const CVec4 &Start, const CVec4 &Stop, float Radius);
|
||
|
|
bool LineInCircle(const CVec4 &Start, const CVec4 &Stop, float Radius, CVec4 &PointOnLine);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// String Operations
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void FromStr(const char *s);
|
||
|
|
void ToStr(char* s) const;
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Debug Routines
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
#ifdef _DEBUG
|
||
|
|
bool IsFinite();
|
||
|
|
bool IsInitialized();
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Data
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
private:
|
||
|
|
float v[4];
|
||
|
|
|
||
|
|
|
||
|
|
public:
|
||
|
|
static const CVec4 mX;
|
||
|
|
static const CVec4 mY;
|
||
|
|
static const CVec4 mZ;
|
||
|
|
static const CVec4 mW;
|
||
|
|
static const CVec4 mZero;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// The 3 Dimensional Vector
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
class CVec3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Constructors
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
#ifndef _DEBUG
|
||
|
|
CVec3() {}
|
||
|
|
#else
|
||
|
|
CVec3() {v[0]=v[1]=v[2]=RAVL_VEC_UDF;} // DEBUG INITIALIZATION
|
||
|
|
#endif
|
||
|
|
CVec3(const float val) {v[0]=val; v[1]=val; v[2]=val; }
|
||
|
|
CVec3(const float x,const float y,const float z) {v[0]=x; v[1]=y; v[2]=z; }
|
||
|
|
CVec3(const CVec3& t) {v[0]=t.v[0]; v[1]=t.v[1]; v[2]=t.v[2];}
|
||
|
|
CVec3(const float *t) {v[0]=t[0]; v[1]=t[1]; v[2]=t[2]; }
|
||
|
|
|
||
|
|
float x() const {return v[0];}
|
||
|
|
float y() const {return v[1];}
|
||
|
|
float z() const {return v[2];}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Initializers
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void Set(const float t) {v[0]=t; v[1]=t; v[2]=t; }
|
||
|
|
void Set(const float *t) {v[0]=t[0]; v[1]=t[1]; v[2]=t[2]; }
|
||
|
|
void Set(const float x,const float y,const float z) {v[0]=x; v[1]=y; v[2]=z; }
|
||
|
|
void Clear() {v[0]=0; v[1]=0; v[2]=0; }
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Member Accessors
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
const float& operator[](int i) const {return v[i];}
|
||
|
|
float& operator[](int i) {return v[i];}
|
||
|
|
float& pitch() {return v[0];}
|
||
|
|
float& yaw() {return v[1];}
|
||
|
|
float& roll() {return v[2];}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Equality / Inequality Operators
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool operator! () const {return !(v[0] && v[1] && v[2] );}
|
||
|
|
bool operator== (const CVec3& t) const {return (v[0]==t.v[0] && v[1]==t.v[1] && v[2]==t.v[2]);}
|
||
|
|
bool operator!= (const CVec3& t) const {return !(v[0]==t.v[0] && v[1]==t.v[1] && v[2]==t.v[2]);}
|
||
|
|
bool operator< (const CVec3& t) const {return (v[0]< t.v[0] && v[1]< t.v[1] && v[2]< t.v[2]);}
|
||
|
|
bool operator> (const CVec3& t) const {return (v[0]> t.v[0] && v[1]> t.v[1] && v[2]> t.v[2]);}
|
||
|
|
bool operator<= (const CVec3& t) const {return (v[0]<=t.v[0] && v[1]<=t.v[1] && v[2]<=t.v[2]);}
|
||
|
|
bool operator>= (const CVec3& t) const {return (v[0]>=t.v[0] && v[1]>=t.v[1] && v[2]>=t.v[2]);}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Basic Arithimitic Operators
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
const CVec3 &operator= (const float d) {v[0]=d; v[1]=d; v[2]=d; return *this;}
|
||
|
|
const CVec3 &operator= (const CVec3& t) {v[0]=t.v[0]; v[1]=t.v[1]; v[2]=t.v[2]; return *this;}
|
||
|
|
|
||
|
|
const CVec3 &operator+= (const float d) {v[0]+=d; v[1]+=d; v[2]+=d; return *this;}
|
||
|
|
const CVec3 &operator+= (const CVec3& t) {v[0]+=t.v[0]; v[1]+=t.v[1]; v[2]+=t.v[2];return *this;}
|
||
|
|
|
||
|
|
const CVec3 &operator-= (const float d) {v[0]-=d; v[1]-=d; v[2]-=d; return *this;}
|
||
|
|
const CVec3 &operator-= (const CVec3& t) {v[0]-=t.v[0]; v[1]-=t.v[1]; v[2]-=t.v[2];return *this;}
|
||
|
|
|
||
|
|
const CVec3 &operator*= (const float d) {v[0]*=d; v[1]*=d; v[2]*=d; return *this;}
|
||
|
|
const CVec3 &operator*= (const CVec3& t) {v[0]*=t.v[0]; v[1]*=t.v[1]; v[2]*=t.v[2];return *this;}
|
||
|
|
|
||
|
|
const CVec3 &operator/= (const float d) {v[0]/=d; v[1]/=d; v[2]/=d; return *this;}
|
||
|
|
const CVec3 &operator/= (const CVec3& t) {v[0]/=t.v[0]; v[1]/=t.v[1]; v[2]/=t.v[2];return *this;}
|
||
|
|
|
||
|
|
inline CVec3 operator+ (const CVec3 &t) const {return CVec3(v[0]+t.v[0], v[1]+t.v[1], v[2]+t.v[2]);}
|
||
|
|
inline CVec3 operator- (const CVec3 &t) const {return CVec3(v[0]-t.v[0], v[1]-t.v[1], v[2]-t.v[2]);}
|
||
|
|
inline CVec3 operator* (const CVec3 &t) const {return CVec3(v[0]*t.v[0], v[1]*t.v[1], v[2]*t.v[2]);}
|
||
|
|
inline CVec3 operator/ (const CVec3 &t) const {return CVec3(v[0]/t.v[0], v[1]/t.v[1], v[2]/t.v[2]);}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Length And Distance Calculations
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float Len() const;
|
||
|
|
float Len2() const {return (v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);}
|
||
|
|
|
||
|
|
float Dist(const CVec3& t) const;
|
||
|
|
float Dist2(const CVec3& t) const {return ((t.v[0]-v[0])*(t.v[0]-v[0]) + (t.v[1]-v[1])*(t.v[1]-v[1]) + (t.v[2]-v[2])*(t.v[2]-v[2]));}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Normalization
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float Norm();
|
||
|
|
float SafeNorm();
|
||
|
|
void AngleNorm();
|
||
|
|
float Truncate(float maxlen);
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Dot, Cross & Perpendicular Vector
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float Dot(const CVec3& t) const {return (v[0]*t.v[0] + v[1]*t.v[1] + v[2]*t.v[2]);}
|
||
|
|
void Cross(const CVec3& t)
|
||
|
|
{
|
||
|
|
CVec3 temp(*this);
|
||
|
|
v[0] = (temp.v[1]*t.v[2]) - (temp.v[2]*t.v[1]);
|
||
|
|
v[1] = (temp.v[2]*t.v[0]) - (temp.v[0]*t.v[2]);
|
||
|
|
v[2] = (temp.v[0]*t.v[1]) - (temp.v[1]*t.v[0]);
|
||
|
|
}
|
||
|
|
void Perp();
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Truncation & Element Analysis
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void Min(const CVec3& t)
|
||
|
|
{
|
||
|
|
if (t.v[0]<v[0]) v[0]=t.v[0];
|
||
|
|
if (t.v[1]<v[1]) v[1]=t.v[1];
|
||
|
|
if (t.v[2]<v[2]) v[2]=t.v[2];
|
||
|
|
}
|
||
|
|
void Max(const CVec3& t)
|
||
|
|
{
|
||
|
|
if (t.v[0]>v[0]) v[0]=t.v[0];
|
||
|
|
if (t.v[1]>v[1]) v[1]=t.v[1];
|
||
|
|
if (t.v[2]>v[2]) v[2]=t.v[2];
|
||
|
|
}
|
||
|
|
float MaxElement() const
|
||
|
|
{
|
||
|
|
return v[MaxElementIndex()];
|
||
|
|
}
|
||
|
|
int MaxElementIndex() const;
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Interpolation
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void Interp(const CVec3 &v1, const CVec3 &v2, const float t)
|
||
|
|
{
|
||
|
|
(*this)=v1;
|
||
|
|
(*this)-=v2;
|
||
|
|
(*this)*=t;
|
||
|
|
(*this)+=v2;
|
||
|
|
}
|
||
|
|
void ScaleAdd(const CVec3& t, const float scale)
|
||
|
|
{
|
||
|
|
v[0] += (scale * t.v[0]);
|
||
|
|
v[1] += (scale * t.v[1]);
|
||
|
|
v[2] += (scale * t.v[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Conversion Angle To Vector (Angle In Degrees)
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void VecToAng();
|
||
|
|
void AngToVec();
|
||
|
|
void AngToVec(CVec3& Right, CVec3& Up);
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Conversion Angle To Vector (Angle In Radians)
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void VecToAngRad();
|
||
|
|
void AngToVecRad();
|
||
|
|
void AngToVecRad(CVec3& Right, CVec3& Up);
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Conversion Between Radians And Degrees
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void ToRadians();
|
||
|
|
void ToDegrees();
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Project
|
||
|
|
//
|
||
|
|
// Standard projection function. Take the (this) and project it onto the vector
|
||
|
|
// (U). Imagine drawing a line perpendicular to U from the endpoint of the (this)
|
||
|
|
// Vector. That then becomes the new vector.
|
||
|
|
//
|
||
|
|
// The value returned is the scale of the new vector with respect to the one passed
|
||
|
|
// to the function. If the scale is less than (1.0) then the new vector is shorter
|
||
|
|
// than (U). If the scale is negative, then the vector is going in the opposite
|
||
|
|
// direction of (U).
|
||
|
|
//
|
||
|
|
// _ (U)
|
||
|
|
// /|
|
||
|
|
// / _ (this)
|
||
|
|
// / RESULTS-> /|
|
||
|
|
// / /
|
||
|
|
// / __\ (this) /
|
||
|
|
// /___--- / /
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float Project(const CVec3 &U)
|
||
|
|
{
|
||
|
|
float Scale = (Dot(U) / U.Len2()); // Find the scale of this vector on U
|
||
|
|
(*this)=U; // Copy U onto this vector
|
||
|
|
(*this)*=Scale; // Use the previously calculated scale to get the right length.
|
||
|
|
return Scale;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Project To Line
|
||
|
|
//
|
||
|
|
// This function takes two other points in space as the start and end of a line
|
||
|
|
// segment and projects the (this) point onto the line defined by (Start)->(Stop)
|
||
|
|
//
|
||
|
|
// RETURN VALUES:
|
||
|
|
// (-INF, 0.0) : (this) landed on the line before (Start)
|
||
|
|
// (0.0, 1.0) : (this) landed in the line segment between (Start) and (Stop)
|
||
|
|
// (1.0, INF) : (this) landed on the line beyond (End)
|
||
|
|
//
|
||
|
|
// (Stop)
|
||
|
|
// /
|
||
|
|
// /
|
||
|
|
// o _
|
||
|
|
// / |\
|
||
|
|
// / (this)
|
||
|
|
// /
|
||
|
|
// (Start)
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float ProjectToLine(const CVec3 &Start, const CVec3 &Stop)
|
||
|
|
{
|
||
|
|
(*this) -= Start;
|
||
|
|
float Scale = Project(Stop - Start);
|
||
|
|
(*this) += Start;
|
||
|
|
return Scale;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Project To Line Seg
|
||
|
|
//
|
||
|
|
// Same As Project To Line, Except It Will Clamp To Start And Stop
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float ProjectToLineSeg(const CVec3 &Start, const CVec3 &Stop)
|
||
|
|
{
|
||
|
|
float Scale = ProjectToLine(Start, Stop);
|
||
|
|
if (Scale<0.0f)
|
||
|
|
{
|
||
|
|
(*this) = Start;
|
||
|
|
}
|
||
|
|
else if (Scale>1.0f)
|
||
|
|
{
|
||
|
|
(*this) = Stop;
|
||
|
|
}
|
||
|
|
return Scale;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Distance To Line
|
||
|
|
//
|
||
|
|
// Uses project to line and than calculates distance to the new point
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float DistToLine(const CVec3 &Start, const CVec3 &Stop) const
|
||
|
|
{
|
||
|
|
CVec3 P(*this);
|
||
|
|
P.ProjectToLineSeg(Start, Stop);
|
||
|
|
|
||
|
|
return Dist(P);
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Distance To Line
|
||
|
|
//
|
||
|
|
// Uses project to line and than calculates distance to the new point
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float DistToLine2(const CVec3 &Start, const CVec3 &Stop) const
|
||
|
|
{
|
||
|
|
CVec3 P(*this);
|
||
|
|
P.ProjectToLineSeg(Start, Stop);
|
||
|
|
|
||
|
|
return Dist2(P);
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Translation & Rotation (2D)
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void RotatePoint(const CVec3 &Angle, const CVec3 &Origin);
|
||
|
|
void Reposition(const CVec3 &Translation, float RotationDegrees=0.0);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Area Of The Parallel Pipid (2D)
|
||
|
|
//
|
||
|
|
// Given two more points, this function calculates the area of the parallel pipid
|
||
|
|
// formed.
|
||
|
|
//
|
||
|
|
// Note: This function CAN return a negative "area" if (this) is above or right of
|
||
|
|
// (A) and (B)... We do not take the abs because the sign of the "area" is needed
|
||
|
|
// for the left right test (see below)
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// ___---( ... )
|
||
|
|
// (A)---/ /
|
||
|
|
// / /
|
||
|
|
// / /
|
||
|
|
// / /
|
||
|
|
// / ___---(B)
|
||
|
|
// (this)---/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float AreaParallelPipid(const CVec3 &A, const CVec3 &B) const
|
||
|
|
{
|
||
|
|
return ((A.v[0]*B.v[1] - A.v[1]*B.v[0]) +
|
||
|
|
(B.v[0]* v[1] - v[0]*B.v[1]) +
|
||
|
|
( v[0]*A.v[1] - A.v[0]* v[1]));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Area Of The Triangle (2D)
|
||
|
|
//
|
||
|
|
// Given two more points, this function calculates the area of the triangle formed.
|
||
|
|
//
|
||
|
|
// (A)
|
||
|
|
// / \__
|
||
|
|
// / \__
|
||
|
|
// / \_
|
||
|
|
// / ___---(B)
|
||
|
|
// (this)---/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
float AreaTriange(const CVec3 &A, const CVec3 &B) const
|
||
|
|
{
|
||
|
|
return (AreaParallelPipid(A, B) * 0.5f);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// The Left Right Test (2D)
|
||
|
|
//
|
||
|
|
// Given a line segment (Start->End) and a tolerance for *right on*, this function
|
||
|
|
// evaluates which side the point is of the line. (Side_Left in this example)
|
||
|
|
//
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// (this) ___---/(End)
|
||
|
|
// ___---/
|
||
|
|
// ___---/
|
||
|
|
// (Start)/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
ESide LRTest(const CVec3 &Start, const CVec3 &End, float Tolerance=0.0) const
|
||
|
|
{
|
||
|
|
float Area = AreaParallelPipid(Start, End);
|
||
|
|
if (Area>Tolerance)
|
||
|
|
{
|
||
|
|
return Side_Left;
|
||
|
|
}
|
||
|
|
if (Area<(Tolerance*-1))
|
||
|
|
{
|
||
|
|
return Side_Right;
|
||
|
|
}
|
||
|
|
return Side_None;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Point In Circumscribed Circle (True/False)
|
||
|
|
//
|
||
|
|
// Returns true if the given point is within the circumscribed
|
||
|
|
// circle of the given ABC Triangle:
|
||
|
|
// _____
|
||
|
|
// / B \
|
||
|
|
// / / \ \
|
||
|
|
// | / \ |
|
||
|
|
// |A---------C|
|
||
|
|
// \ Pt /
|
||
|
|
// \_______/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool PtInCircle(const CVec3 &A, const CVec3 &B, const CVec3 &C) const;
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Point In Standard Circle (True/False)
|
||
|
|
//
|
||
|
|
// Returns true if the given point is within the Circle
|
||
|
|
// _____
|
||
|
|
// / \
|
||
|
|
// / \
|
||
|
|
// | Circle |
|
||
|
|
// | |
|
||
|
|
// \ Pt /
|
||
|
|
// \_______/
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool PtInCircle(const CVec3 &Circle, float Radius) const;
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Line Intersects Circle (True/False)
|
||
|
|
//
|
||
|
|
// r - Radius Of The Circle
|
||
|
|
// A - Start Of Line Segment
|
||
|
|
// B - End Of Line Segment
|
||
|
|
//
|
||
|
|
// P - Projected Position Of Origin Onto Line AB
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// (Stop)
|
||
|
|
// /
|
||
|
|
// /
|
||
|
|
// (P)
|
||
|
|
// / \ \
|
||
|
|
// / (this)-r->|
|
||
|
|
// / /
|
||
|
|
// (Start)
|
||
|
|
//
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
bool LineInCircle(const CVec3 &Start, const CVec3 &Stop, float Radius);
|
||
|
|
bool LineInCircle(const CVec3 &Start, const CVec3 &Stop, float Radius, CVec3 &PointOnLine);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// String Operations
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
void FromStr(const char *s);
|
||
|
|
void ToStr(char* s) const;
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Debug Routines
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
#ifdef _DEBUG
|
||
|
|
bool IsFinite();
|
||
|
|
bool IsInitialized();
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Data
|
||
|
|
////////////////////////////////////////////////////////////////////////////////////
|
||
|
|
|
||
|
|
public:
|
||
|
|
float v[3];
|
||
|
|
static const CVec3 mX;
|
||
|
|
static const CVec3 mY;
|
||
|
|
static const CVec3 mZ;
|
||
|
|
static const CVec3 mZero;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
//};
|
||
|
|
#endif
|