518 lines
11 KiB
C++
518 lines
11 KiB
C++
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//========= Copyright <20> 1996-2005, Valve Corporation, All rights reserved. ============//
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//
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// Purpose: Math functions specific to the editor.
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//
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//=============================================================================//
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#include "hammer_mathlib.h"
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#include <string.h>
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#include <Windows.h>
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// memdbgon must be the last include file in a .cpp file!!!
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#include <tier0/memdbgon.h>
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// provide implementation for mathlib Sys_Error()
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extern void Error(char* fmt, ...);
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extern "C" void Sys_Error( char *error, ... )
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{
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Error( "%s", error );
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}
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static int s_BoxFaces[6][3] =
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{
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{ 0, 4, 2 },
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{ 4, 5, 6 },
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{ 5, 1, 7 },
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{ 1, 0, 3 },
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{ 2, 6, 3 },
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{ 5, 4, 1 },
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};
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void polyMake( float x1, float y1, float x2, float y2, int npoints, float start_ang, Vector *pmPoints )
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{
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int point;
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double angle = start_ang, angle_delta = 360.0 / (double) npoints;
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double xrad = (x2-x1) / 2, yrad = (y2-y1) / 2;
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// make centerpoint for polygon:
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float xCenter = x1 + xrad;
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float yCenter = y1 + yrad;
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for( point = 0; point < npoints; point++, angle += angle_delta )
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{
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if( angle > 360 )
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angle -= 360;
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pmPoints[point][0] = rint(xCenter + (sin(DEG2RAD(angle)) * (float)xrad));
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pmPoints[point][1] = rint(yCenter + (cos(DEG2RAD(angle)) * (float)yrad));
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}
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pmPoints[point][0] = pmPoints[0][0];
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pmPoints[point][1] = pmPoints[0][1];
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}
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float fixang(float a)
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{
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if(a < 0.0)
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return a+360.0;
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if(a > 359.9)
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return a-360.0;
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return a;
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}
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float lineangle(float x1, float y1, float x2, float y2)
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{
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float x, y;
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float rvl;
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x = x2 - x1;
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y = y2 - y1;
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if(!x && !y)
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return 0.0;
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rvl = RAD2DEG(atan2( y, x ));
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return (rvl);
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}
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#if !defined(_MSC_VER) || _MSC_VER < 1800
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// This C99 function exists in VS 2013's math.h but are not currently available elsewhere.
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float rint(float f)
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{
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if (f > 0.0f) {
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return (float) floor(f + 0.5f);
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} else if (f < 0.0f) {
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return (float) ceil(f - 0.5f);
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} else
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return 0.0f;
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}
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#endif
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//-----------------------------------------------------------------------------
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// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
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//
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// | ax2 + (1 - ax2)cosQ axay(1 - cosQ) - azsinQ azax(1 - cosQ) + aysinQ |
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// Ra(Q) = | axay(1 - cosQ) + azsinQ ay2 + (1 - ay2)cosQ ayaz(1 - cosQ) - axsinQ |
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// | azax(1 - cosQ) - aysinQ ayaz(1 - cosQ) + axsinQ az2 + (1 - az2)cosQ |
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//
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// Input : Matrix -
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// Axis -
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// fAngle -
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//-----------------------------------------------------------------------------
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void AxisAngleMatrix(VMatrix& Matrix, const Vector& Axis, float fAngle)
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{
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float fRadians;
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float fAxisXSquared;
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float fAxisYSquared;
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float fAxisZSquared;
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float fSin;
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float fCos;
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fRadians = fAngle * M_PI / 180.0;
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fSin = sin(fRadians);
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fCos = cos(fRadians);
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fAxisXSquared = Axis[0] * Axis[0];
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fAxisYSquared = Axis[1] * Axis[1];
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fAxisZSquared = Axis[2] * Axis[2];
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// Column 0:
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Matrix[0][0] = fAxisXSquared + (1 - fAxisXSquared) * fCos;
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Matrix[1][0] = Axis[0] * Axis[1] * (1 - fCos) + Axis[2] * fSin;
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Matrix[2][0] = Axis[2] * Axis[0] * (1 - fCos) - Axis[1] * fSin;
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Matrix[3][0] = 0;
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// Column 1:
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Matrix[0][1] = Axis[0] * Axis[1] * (1 - fCos) - Axis[2] * fSin;
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Matrix[1][1] = fAxisYSquared + (1 - fAxisYSquared) * fCos;
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Matrix[2][1] = Axis[1] * Axis[2] * (1 - fCos) + Axis[0] * fSin;
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Matrix[3][1] = 0;
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// Column 2:
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Matrix[0][2] = Axis[2] * Axis[0] * (1 - fCos) + Axis[1] * fSin;
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Matrix[1][2] = Axis[1] * Axis[2] * (1 - fCos) - Axis[0] * fSin;
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Matrix[2][2] = fAxisZSquared + (1 - fAxisZSquared) * fCos;
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Matrix[3][2] = 0;
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// Column 3:
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Matrix[0][3] = 0;
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Matrix[1][3] = 0;
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Matrix[2][3] = 0;
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Matrix[3][3] = 1;
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}
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void RotateAroundAxis(VMatrix& Matrix, float fDegrees, int nAxis)
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{
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int a,b;
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if ( fDegrees == 0 )
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return;
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if ( nAxis == 0 )
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{
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a=1; b=2;
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}
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else if ( nAxis == 1)
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{
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a=0;b=2;
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}
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else
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{
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a=0; b=1;
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}
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float fRadians = DEG2RAD(fDegrees);
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float fSin = (float)sin(fRadians);
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float fCos = (float)cos(fRadians);
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if ( nAxis == 1 )
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fSin = -fSin;
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float Temp0a = Matrix[0][a] * fCos + Matrix[0][b] * fSin;
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float Temp1a = Matrix[1][a] * fCos + Matrix[1][b] * fSin;
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float Temp2a = Matrix[2][a] * fCos + Matrix[2][b] * fSin;
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float Temp3a = Matrix[3][a] * fCos + Matrix[3][b] * fSin;
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if ( nAxis == 1 )
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fSin = -fSin;
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float Temp0b = Matrix[0][a] * -fSin + Matrix[0][b] * fCos;
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float Temp1b = Matrix[1][a] * -fSin + Matrix[1][b] * fCos;
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float Temp2b = Matrix[2][a] * -fSin + Matrix[2][b] * fCos;
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float Temp3b = Matrix[3][a] * -fSin + Matrix[3][b] * fCos;
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Matrix[0][a] = Temp0a;
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Matrix[1][a] = Temp1a;
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Matrix[2][a] = Temp2a;
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Matrix[3][a] = Temp3a;
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Matrix[0][b] = Temp0b;
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Matrix[1][b] = Temp1b;
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Matrix[2][b] = Temp2b;
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Matrix[3][b] = Temp3b;
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}
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//-----------------------------------------------------------------------------
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// Purpose:
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// Input : pt1 -
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// pt2 -
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// x1 -
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// y1 -
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// x2 -
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// y2 -
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//-----------------------------------------------------------------------------
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bool IsLineInside(const Vector2D &pt1, const Vector2D &pt2, int x1, int y1, int x2, int y2)
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{
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int lx1 = pt1.x;
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int ly1 = pt1.y;
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int lx2 = pt2.x;
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int ly2 = pt2.y;
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int i;
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// is the line totally on one side of the box?
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if( (lx2 > x2 && lx1 > x2) ||
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(lx2 < x1 && lx1 < x1) ||
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(ly2 > y2 && ly1 > y2) ||
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(ly2 < y1 && ly1 < y1) )
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return false;
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if( lx1 >= x1 && lx1 <= x2 && ly1 >= y1 && ly1 <= y2 )
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return true; // the first point is inside the box
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if( lx2 >= x1 && lx2 <= x2 && ly2 >= y1 && ly2 <= y2 )
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return true; // the second point is inside the box
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if( (ly1 > y1) != (ly2 > y1) )
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{
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i = lx1 + (int) ( (long) (y1 - ly1) * (long) (lx2 - lx1) / (long) (ly2 - ly1));
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if( i >= x1 && i <= x2 )
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return true; // the line crosses the y1 side (left)
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}
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if( (ly1 > y2) != (ly2 > y2))
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{
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i = lx1 + (int) ( (long) (y2 - ly1) * (long) (lx2 - lx1) / (long) (ly2 - ly1));
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if( i >= x1 && i <= x2 )
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return true; // the line crosses the y2 side (right)
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}
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if( (lx1 > x1) != (lx2 > x1))
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{
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i = ly1 + (int) ( (long) (x1 - lx1) * (long) (ly2 - ly1) / (long) (lx2 - lx1));
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if( i >= y1 && i <= y2 )
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return true; // the line crosses the x1 side (down)
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}
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if( (lx1 > x2) != (lx2 > x2))
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{
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i = ly1 + (int) ( (long) (x2 - lx1) * (long) (ly2 - ly1) / (long) (lx2 - lx1));
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if( i >= y1 && i <= y2 )
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return true; // the line crosses the x2 side (up)
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}
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// The line does not intersect the box.
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return false;
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}
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bool IsPointInside(const Vector2D &pt, const Vector2D &mins, const Vector2D &maxs )
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{
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return ( pt.x >= mins.x ) && ( pt.y >= mins.y ) && ( pt.x <= maxs.x ) && ( pt.y <= maxs.y );
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}
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// Is box 1 inside box 2?
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bool IsBoxInside( const Vector2D &min1, const Vector2D &max1, const Vector2D &min2, const Vector2D &max2 )
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{
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if ( ( min1.x < min2.x ) || ( max1.x > max2.x ) )
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return false;
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if ( ( min1.y < min2.y ) || ( max1.y > max2.y ) )
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return false;
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return true;
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}
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bool IsBoxIntersecting( const Vector2D &min1, const Vector2D &max1, const Vector2D &min2, const Vector2D &max2 )
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{
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if ( ( min1.x >= max2.x ) || ( max1.x <= min2.x ) )
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return false;
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if ( ( min1.y >= max2.y ) || ( max1.y <= min2.y ) )
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return false;
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return true;
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}
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void NormalizeBox( Vector &mins, Vector &maxs )
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{
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for (int i=0; i<3; i++ )
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{
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if ( mins[i] > maxs[i])
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{
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V_swap( mins[i], maxs[i] );
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}
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}
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}
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void NormalizeBox( Vector2D &mins, Vector2D &maxs )
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{
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if ( mins.x > maxs.x )
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{
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V_swap( mins.x, maxs.x );
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}
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if ( mins.y > maxs.y )
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{
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V_swap( mins.y, maxs.y );
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}
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}
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bool IsValidBox( Vector &mins, Vector &maxs )
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{
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return ( mins.x <= maxs.x ) && ( mins.y <= maxs.y ) && ( mins.z <= maxs.z );
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}
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bool IsValidBox( const Vector2D &mins, const Vector2D &maxs )
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{
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return ( mins.x <= maxs.x ) && ( mins.y <= maxs.y );
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}
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void LimitBox( Vector &mins, Vector &maxs, float limit )
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{
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for ( int i=0; i<3;i++)
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{
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if ( mins[i] < -limit )
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mins[i] = -limit;
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if ( maxs[i] > limit )
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maxs[i] = limit;
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}
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}
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void GetAxisFromFace( int nFace, Vector& vHorz, Vector &vVert, Vector &vThrd )
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{
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Assert( nFace >= 0 && nFace < 6);
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Vector points[8];
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PointsFromBox( Vector(0,0,0), Vector(1,1,1), points );
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Vector p1 = points[s_BoxFaces[nFace][0]];
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Vector p2 = points[s_BoxFaces[nFace][1]];
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Vector p3 = points[s_BoxFaces[nFace][2]];
|
|||
|
|
|
|||
|
|
// compose equation
|
|||
|
|
vHorz = p2 - p1;
|
|||
|
|
vVert = p3 - p1;
|
|||
|
|
vThrd = CrossProduct( vHorz, vVert );
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
float IntersectionLineAABBox( const Vector& mins, const Vector& maxs, const Vector& vStart, const Vector& vEnd, int &nFace )
|
|||
|
|
{
|
|||
|
|
Vector vz = vEnd - vStart;
|
|||
|
|
|
|||
|
|
// quick distance check first
|
|||
|
|
Vector vCenter = (mins+maxs)/2;
|
|||
|
|
Vector vTmp = maxs-vCenter;
|
|||
|
|
float radius = DotProduct(vTmp,vTmp);
|
|||
|
|
vTmp = CrossProduct(vz,(vStart-vCenter));
|
|||
|
|
float dist = DotProduct( vTmp,vTmp ) / DotProduct( vz,vz );
|
|||
|
|
|
|||
|
|
nFace = -1;
|
|||
|
|
|
|||
|
|
if ( dist > radius )
|
|||
|
|
{
|
|||
|
|
return -1;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// ok, now check against all 6 faces
|
|||
|
|
Vector points[8];
|
|||
|
|
PointsFromBox( mins, maxs, points );
|
|||
|
|
|
|||
|
|
vz = -vz;
|
|||
|
|
|
|||
|
|
float fDistance = 999999;
|
|||
|
|
|
|||
|
|
for ( int i=0; i<6; i++ )
|
|||
|
|
{
|
|||
|
|
// get points of face
|
|||
|
|
Vector p1 = points[s_BoxFaces[i][0]];
|
|||
|
|
Vector p2 = points[s_BoxFaces[i][1]];
|
|||
|
|
Vector p3 = points[s_BoxFaces[i][2]];
|
|||
|
|
|
|||
|
|
// compose equation
|
|||
|
|
Vector v0 = vStart - p1;
|
|||
|
|
Vector vx = p2 - p1;
|
|||
|
|
Vector vy = p3 - p1;
|
|||
|
|
|
|||
|
|
Vector vOut;
|
|||
|
|
|
|||
|
|
// solve equation v0 = x*v1 + y*v2 + z*v3
|
|||
|
|
if ( !SolveLinearEquation( v0, vx, vy, vz, vOut) )
|
|||
|
|
continue;
|
|||
|
|
|
|||
|
|
if ( vOut.z < 0 || vOut.z > 1 )
|
|||
|
|
continue;
|
|||
|
|
|
|||
|
|
if ( vOut.x < 0 || vOut.x > 1 )
|
|||
|
|
continue;
|
|||
|
|
|
|||
|
|
if ( vOut.y < 0 || vOut.y > 1 )
|
|||
|
|
continue;
|
|||
|
|
|
|||
|
|
if ( vOut.z < fDistance )
|
|||
|
|
{
|
|||
|
|
nFace = i;
|
|||
|
|
fDistance = vOut.z;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if ( nFace >= 0 )
|
|||
|
|
{
|
|||
|
|
return fDistance*VectorLength(vz);
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
return -1;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
void RoundVector( Vector2D &v )
|
|||
|
|
{
|
|||
|
|
v.x = (int)(v.x+0.5f);
|
|||
|
|
v.y = (int)(v.y+0.5f);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void PointsRevertOrder( Vector *pPoints, int nPoints)
|
|||
|
|
{
|
|||
|
|
Vector *tmpPoints = (Vector*)_alloca( sizeof(Vector)*nPoints );
|
|||
|
|
memcpy( tmpPoints, pPoints, sizeof(Vector)*nPoints );
|
|||
|
|
for ( int i = 0; i<nPoints; i++)
|
|||
|
|
{
|
|||
|
|
pPoints[i] = tmpPoints[nPoints-i-1];
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
const Vector &GetNormalFromFace( int nFace )
|
|||
|
|
{
|
|||
|
|
// ok, now check against all 6 faces
|
|||
|
|
|
|||
|
|
Vector points[8];
|
|||
|
|
|
|||
|
|
Assert( nFace>=0 && nFace<6 );
|
|||
|
|
|
|||
|
|
PointsFromBox( Vector(0,0,0), Vector(1,1,1), points );
|
|||
|
|
|
|||
|
|
return GetNormalFromPoints( points[s_BoxFaces[nFace][0]], points[s_BoxFaces[nFace][1]],points[s_BoxFaces[nFace][2]] );
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
const Vector &GetNormalFromPoints( const Vector &p0, const Vector &p1, const Vector &p2 )
|
|||
|
|
{
|
|||
|
|
static Vector vNormal;
|
|||
|
|
Vector v1 = p0 - p1;
|
|||
|
|
Vector v2 = p2 - p1;
|
|||
|
|
CrossProduct(v1, v2, vNormal);
|
|||
|
|
VectorNormalize(vNormal);
|
|||
|
|
return vNormal;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// solve equation v0 = x*v1 + y*v2 + z*v3
|
|||
|
|
bool SolveLinearEquation( const Vector& v0, const Vector& v1, const Vector& v2, const Vector& v3, Vector& vOut)
|
|||
|
|
{
|
|||
|
|
VMatrix matrix, inverse;
|
|||
|
|
matrix.Init(
|
|||
|
|
v1.x, v1.y, v1.z, 0,
|
|||
|
|
v2.x, v2.y, v2.z, 0,
|
|||
|
|
v3.x, v3.y, v3.z, 0,
|
|||
|
|
0.0f, 0.0f, 0.0f, 1
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
if( !matrix.InverseGeneral(inverse) )
|
|||
|
|
return false;
|
|||
|
|
|
|||
|
|
vOut = inverse.VMul3x3Transpose( v0 );
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
bool BuildAxesFromNormal( const Vector &vNormal, Vector &vHorz, Vector &vVert )
|
|||
|
|
{
|
|||
|
|
vHorz.Init();
|
|||
|
|
vVert.Init();
|
|||
|
|
|
|||
|
|
// find the major axis
|
|||
|
|
float bestMin = 99999;
|
|||
|
|
int bestAxis = -1;
|
|||
|
|
for (int i=0 ; i<3; i++)
|
|||
|
|
{
|
|||
|
|
float a = fabs(vNormal[i]);
|
|||
|
|
if (a < bestMin)
|
|||
|
|
{
|
|||
|
|
bestAxis = i;
|
|||
|
|
bestMin = a;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (bestAxis==-1)
|
|||
|
|
return false;
|
|||
|
|
|
|||
|
|
vHorz[bestAxis] = 1;
|
|||
|
|
|
|||
|
|
CrossProduct( vNormal,vHorz,vVert);
|
|||
|
|
CrossProduct( vNormal,vVert,vHorz);
|
|||
|
|
|
|||
|
|
VectorNormalize( vHorz );
|
|||
|
|
VectorNormalize( vVert );
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|