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-/* Starshatter OpenSource Distribution
- Copyright (c) 1997-2004, Destroyer Studios LLC.
- All Rights Reserved.
-
- Redistribution and use in source and binary forms, with or without
- modification, are permitted provided that the following conditions are met:
-
- * Redistributions of source code must retain the above copyright notice,
- this list of conditions and the following disclaimer.
- * Redistributions in binary form must reproduce the above copyright notice,
- this list of conditions and the following disclaimer in the documentation
- and/or other materials provided with the distribution.
- * Neither the name "Destroyer Studios" nor the names of its contributors
- may be used to endorse or promote products derived from this software
- without specific prior written permission.
-
- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
- AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
- LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
- CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
- SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
- INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
- CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
- POSSIBILITY OF SUCH DAMAGE.
-
- SUBSYSTEM: nGenEx.lib
- FILE: Geometry.cpp
- AUTHOR: John DiCamillo
-
-
- OVERVIEW
- ========
- Geometric Utilities
-*/
-
-#include "MemDebug.h"
-#include "Geometry.h"
-
-// +--------------------------------------------------------------------+
-
-void Rect::Inflate(int dx, int dy)
-{
- x -= dx;
- w += dx*2;
- y -= dy;
- h += dy*2;
-}
-
-void Rect::Deflate(int dx, int dy)
-{
- x += dx;
- w -= dx*2;
- y += dy;
- h -= dy*2;
-}
-
-void Rect::Inset(int l, int r, int t, int b)
-{
- x += l;
- y += t;
- w -= l + r;
- h -= t + b;
-}
-
-int Rect::Contains(int ax, int ay) const
-{
- if (ax < x) return 0;
- if (ax > x+w) return 0;
- if (ay < y) return 0;
- if (ay > y+h) return 0;
-
- return 1;
-}
-
-// +--------------------------------------------------------------------+
-
-double
-Point::Normalize()
-{
- double scale = 1.0;
- double len = length();
-
- if (len)
- scale /= len;
-
- x *= scale;
- y *= scale;
- z *= scale;
-
- return len;
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Point::SetElement(int i, double v)
-{
- switch (i) {
- case 0: x = v; break;
- case 1: y = v; break;
- case 2: z = v; break;
- default: break;
- }
-}
-
-// +--------------------------------------------------------------------+
-
-Point
-Point::operator*(const Matrix& m) const
-{
- Point result;
-
- result.x = (m.elem[0][0] * x) + (m.elem[1][0] * y) + (m.elem[2][0] * z);
- result.y = (m.elem[0][1] * x) + (m.elem[1][1] * y) + (m.elem[2][1] * z);
- result.z = (m.elem[0][2] * x) + (m.elem[1][2] * y) + (m.elem[2][2] * z);
-
- return result;
-}
-
-// +--------------------------------------------------------------------+
-
-double ClosestApproachTime(const Point& loc1, const Point& vel1,
-const Point& loc2, const Point& vel2)
-{
- double t = 0;
-
- Point D = loc1-loc2;
- Point Dv = vel1-vel2;
-
- if (Dv.x || Dv.y || Dv.z)
- t = -1 * (Dv*D) / (Dv*Dv);
-
- return t;
-}
-
-// +--------------------------------------------------------------------+
-
-float
-Vec2::Normalize()
-{
- float scale = 1.0f;
- float len = length();
-
- if (len)
- scale /= len;
-
- x *= scale;
- y *= scale;
-
- return len;
-}
-
-// +--------------------------------------------------------------------+
-
-float
-Vec3::Normalize()
-{
- float scale = 1.0f;
- float len = length();
-
- if (len)
- scale /= len;
-
- x *= scale;
- y *= scale;
- z *= scale;
-
- return len;
-}
-
-// +--------------------------------------------------------------------+
-
-Vec3
-Vec3::operator*(const Matrix& m) const
-{
- Vec3 result;
-
- result.x = (float) ((m.elem[0][0] * x) + (m.elem[1][0] * y) + (m.elem[2][0] * z));
- result.y = (float) ((m.elem[0][1] * x) + (m.elem[1][1] * y) + (m.elem[2][1] * z));
- result.z = (float) ((m.elem[0][2] * x) + (m.elem[1][2] * y) + (m.elem[2][2] * z));
-
- return result;
-}
-
-// +--------------------------------------------------------------------+
-
-double ClosestApproachTime(const Vec3& loc1, const Vec3& vel1,
-const Vec3& loc2, const Vec3& vel2)
-{
- double t = 0;
-
- Point D = loc1-loc2;
- Point Dv = vel1-vel2;
-
- if (Dv.x || Dv.y || Dv.z)
- t = -1 * (Dv*D) / (Dv*Dv);
-
- return t;
-}
-
-// +--------------------------------------------------------------------+
-
-double
-Quaternion::Normalize()
-{
- double scale = 1.0;
- double len = length();
-
- if (len)
- scale /= len;
-
- x *= scale;
- y *= scale;
- z *= scale;
- w *= scale;
-
- return len;
-}
-
-// +--------------------------------------------------------------------+
-
-Matrix::Matrix()
-{
- Identity();
-}
-
-Matrix::Matrix(const Matrix& m)
-{
- CopyMemory(elem, m.elem, sizeof(elem));
-}
-
-Matrix::Matrix(const Point& vrt, const Point& vup, const Point& vpn)
-{
- elem[0][0] = vrt.x;
- elem[0][1] = vrt.y;
- elem[0][2] = vrt.z;
-
- elem[1][0] = vup.x;
- elem[1][1] = vup.y;
- elem[1][2] = vup.z;
-
- elem[2][0] = vpn.x;
- elem[2][1] = vpn.y;
- elem[2][2] = vpn.z;
-}
-
-// +--------------------------------------------------------------------+
-
-Matrix&
-Matrix::operator =(const Matrix& m)
-{
- CopyMemory(elem, m.elem, sizeof(elem));
-
- return *this;
-}
-
-// +--------------------------------------------------------------------+
-
-Matrix&
-Matrix::operator*=(const Matrix& m)
-{
- return *this = *this * m;
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Identity()
-{
- elem[0][0] = 1;
- elem[0][1] = 0;
- elem[0][2] = 0;
-
- elem[1][0] = 0;
- elem[1][1] = 1;
- elem[1][2] = 0;
-
- elem[2][0] = 0;
- elem[2][1] = 0;
- elem[2][2] = 1;
-}
-
-// +--------------------------------------------------------------------+
-
-inline void swap_elem(double& a, double& b) { double t=a; a=b; b=t; }
-
-void
-Matrix::Transpose()
-{
- swap_elem(elem[0][1], elem[1][0]);
- swap_elem(elem[0][2], elem[2][0]);
- swap_elem(elem[1][2], elem[2][1]);
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Rotate(double roll, double pitch, double yaw)
-{
- double e[3][3];
- CopyMemory(e, elem, sizeof(elem));
-
- double sr = sin(roll);
- double cr = cos(roll);
- double sp = sin(pitch);
- double cp = cos(pitch);
- double sy = sin(yaw);
- double cy = cos(yaw);
-
- double a,b,c;
-
- a = cy*cr;
- b = cy*sr;
- c = -sy;
-
- elem[0][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
- elem[0][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
- elem[0][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];
-
- a = cp*-sr + sp*sy*cr;
- b = cp* cr + sp*sy*sr;
- c = sp*cy;
-
- elem[1][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
- elem[1][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
- elem[1][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];
-
- a = -sp*-sr + cp*sy*cr;
- b = -sp* cr + cp*sy*sr;
- c = cp*cy;
-
- elem[2][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
- elem[2][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
- elem[2][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Roll(double roll)
-{
- double s = sin(roll);
- double c = cos(roll);
-
- double e00 = elem[0][0];
- double e01 = elem[0][1];
- double e02 = elem[0][2];
- double e10 = elem[1][0];
- double e11 = elem[1][1];
- double e12 = elem[1][2];
-
- elem[0][0] = c*e00 + s*e10;
- elem[0][1] = c*e01 + s*e11;
- elem[0][2] = c*e02 + s*e12;
-
- elem[1][0] = -s*e00 + c*e10;
- elem[1][1] = -s*e01 + c*e11;
- elem[1][2] = -s*e02 + c*e12;
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Pitch(double pitch)
-{
- double s = sin(pitch);
- double c = cos(pitch);
-
- double e10 = elem[1][0];
- double e11 = elem[1][1];
- double e12 = elem[1][2];
- double e20 = elem[2][0];
- double e21 = elem[2][1];
- double e22 = elem[2][2];
-
- elem[1][0] = c*e10 + s*e20;
- elem[1][1] = c*e11 + s*e21;
- elem[1][2] = c*e12 + s*e22;
-
- elem[2][0] = -s*e10 + c*e20;
- elem[2][1] = -s*e11 + c*e21;
- elem[2][2] = -s*e12 + c*e22;
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Yaw(double yaw)
-{
- double s = sin(yaw);
- double c = cos(yaw);
-
- double e00 = elem[0][0];
- double e01 = elem[0][1];
- double e02 = elem[0][2];
- double e20 = elem[2][0];
- double e21 = elem[2][1];
- double e22 = elem[2][2];
-
- elem[0][0] = c*e00 - s*e20;
- elem[0][1] = c*e01 - s*e21;
- elem[0][2] = c*e02 - s*e22;
-
- elem[2][0] = s*e00 + c*e20;
- elem[2][1] = s*e01 + c*e21;
- elem[2][2] = s*e02 + c*e22;
-}
-
-// +--------------------------------------------------------------------+
-
-inline int sign(double d) { return (d >= 0); }
-
-void
-Matrix::ComputeEulerAngles(double& roll, double& pitch, double& yaw) const
-{
- double cy;
-
- yaw = asin(-elem[0][2]);
- cy = cos(yaw);
- roll = asin(elem[0][1] / cy);
- pitch = asin(elem[1][2] / cy);
-
- if (sign(cos(roll)*cy) != sign(elem[0][0]))
- roll = PI - roll;
-
- if (sign(cos(pitch)*cy) != sign(elem[2][2]))
- pitch = PI - pitch;
-}
-
-// +--------------------------------------------------------------------+
-
-Matrix
-Matrix::operator*(const Matrix& m) const
-{
- Matrix r;
-
- r.elem[0][0] = elem[0][0]*m.elem[0][0] + elem[0][1]*m.elem[1][0] + elem[0][2]*m.elem[2][0];
- r.elem[0][1] = elem[0][0]*m.elem[0][1] + elem[0][1]*m.elem[1][1] + elem[0][2]*m.elem[2][1];
- r.elem[0][2] = elem[0][0]*m.elem[0][2] + elem[0][1]*m.elem[1][2] + elem[0][2]*m.elem[2][2];
-
- r.elem[1][0] = elem[1][0]*m.elem[0][0] + elem[1][1]*m.elem[1][0] + elem[1][2]*m.elem[2][0];
- r.elem[1][1] = elem[1][0]*m.elem[0][1] + elem[1][1]*m.elem[1][1] + elem[1][2]*m.elem[2][1];
- r.elem[1][2] = elem[1][0]*m.elem[0][2] + elem[1][1]*m.elem[1][2] + elem[1][2]*m.elem[2][2];
-
- r.elem[2][0] = elem[2][0]*m.elem[0][0] + elem[2][1]*m.elem[1][0] + elem[2][2]*m.elem[2][0];
- r.elem[2][1] = elem[2][0]*m.elem[0][1] + elem[2][1]*m.elem[1][1] + elem[2][2]*m.elem[2][1];
- r.elem[2][2] = elem[2][0]*m.elem[0][2] + elem[2][1]*m.elem[1][2] + elem[2][2]*m.elem[2][2];
-
- return r;
-}
-
-// +--------------------------------------------------------------------+
-
-Point
-Matrix::operator*(const Point& p) const
-{
- Point result;
-
- result.x = (elem[0][0] * p.x) + (elem[0][1] * p.y) + (elem[0][2] * p.z);
- result.y = (elem[1][0] * p.x) + (elem[1][1] * p.y) + (elem[1][2] * p.z);
- result.z = (elem[2][0] * p.x) + (elem[2][1] * p.y) + (elem[2][2] * p.z);
-
- return result;
-}
-
-// +--------------------------------------------------------------------+
-
-Vec3
-Matrix::operator*(const Vec3& v) const
-{
- Vec3 result;
-
- result.x = (float) ((elem[0][0] * v.x) + (elem[0][1] * v.y) + (elem[0][2] * v.z));
- result.y = (float) ((elem[1][0] * v.x) + (elem[1][1] * v.y) + (elem[1][2] * v.z));
- result.z = (float) ((elem[2][0] * v.x) + (elem[2][1] * v.y) + (elem[2][2] * v.z));
-
- return result;
-}
-
-// +--------------------------------------------------------------------+
-
-double
-Matrix::Cofactor(int i, int j) const
-{
- int i1=0;
- int i2=2;
- int j1=0;
- int j2=2;
-
- if (i==0) i1=1; else if (i==2) i2=1;
- if (j==0) j1=1; else if (j==2) j2=1;
-
- double factor = elem[i1][j1]*elem[i2][j2] - elem[i1][j2]*elem[i2][j1];
-
- if ((i+j) & 1)
- factor *= -1;
-
- return factor;
-}
-
-// +--------------------------------------------------------------------+
-
-void
-Matrix::Invert()
-{
- double f[3][3];
- int i, j;
-
- for (i = 0; i < 3; i++)
- for (j = 0; j < 3; j++)
- f[i][j] = Cofactor(j,i);
-
- double det = elem[0][0] * f[0][0] +
- elem[0][1] * f[1][0] +
- elem[0][2] * f[2][0];
-
- if (det != 0) {
- double inv = 1/det;
-
- for (i = 0; i < 3; i++)
- for (j = 0; j < 3; j++)
- elem[i][j] = f[i][j] * inv;
- }
-}
-
-// +--------------------------------------------------------------------+
-// +--------------------------------------------------------------------+
-// +--------------------------------------------------------------------+
-
-Plane::Plane()
-: distance(0.0f)
-{ }
-
-Plane::Plane(const Point& p0, const Point& p1, const Point& p2)
-{
- Point d1 = p1 - p0;
- Point d2 = p2 - p0;
-
- normal = (Vec3) d1.cross(d2);
- normal.Normalize();
-
- distance = (float) (normal * p0);
-}
-
-Plane::Plane(const Vec3& v0, const Vec3& v1, const Vec3& v2)
-{
- Vec3 d1 = v1 - v0;
- Vec3 d2 = v2 - v0;
-
- normal = d1.cross(d2);
- normal.Normalize();
-
- distance = normal * v0;
-}
-
-void Plane::Rotate(const Vec3& v0, const Matrix& m)
-{
- normal = normal * m;
- distance = normal * v0;
-}
-
-void Plane::Translate(const Vec3& v0)
-{
- distance = normal * v0;
-}
-
-// +--------------------------------------------------------------------+
-// 3-D dot product.
-
-double DotProduct(const Point& a, const Point& b)
-{
- return (a.x * b.x) + (a.y * b.y) + (a.z * b.z);
-}
-
-// +--------------------------------------------------------------------+
-// 3-D cross product.
-
-void CrossProduct(const Point& a, const Point& b, Point& out)
-{
- out.x = (a.y * b.z) - (a.z * b.y);
- out.y = (a.z * b.x) - (a.x * b.z);
- out.z = (a.x * b.y) - (a.y * b.x);
-}
-
-// +--------------------------------------------------------------------+
-// Concatenate two 3x3 matrices.
-
-void MConcat(double in1[3][3], double in2[3][3], double out[3][3])
-{
- int i, j;
-
- for (i=0 ; i<3 ; i++) {
- for (j=0 ; j<3 ; j++) {
- out[i][j] = in1[i][0] * in2[0][j] +
- in1[i][1] * in2[1][j] +
- in1[i][2] * in2[2][j];
- }
- }
-}
-
-/* GRAPHICS GEMS II ----------------------------------------------------
-*
-* lines_intersect: AUTHOR: Mukesh Prasad
-*
-* This function computes whether two line segments,
-* respectively joining the input points (x1,y1) -- (x2,y2)
-* and the input points (x3,y3) -- (x4,y4) intersect.
-* If the lines intersect, the output variables x, y are
-* set to coordinates of the point of intersection.
-*
-* All values are in integers. The returned value is rounded
-* to the nearest integer point.
-*
-* If non-integral grid points are relevant, the function
-* can easily be transformed by substituting floating point
-* calculations instead of integer calculations.
-*
-* Entry
-* x1, y1, x2, y2 Coordinates of endpoints of one segment.
-* x3, y3, x4, y4 Coordinates of endpoints of other segment.
-*
-* Exit
-* x, y Coordinates of intersection point.
-*
-* The value returned by the function is one of:
-*
-* DONT_INTERSECT 0
-* DO_INTERSECT 1
-* COLLINEAR 2
-*
-* Error conditions:
-*
-* Depending upon the possible ranges, and particularly on 16-bit
-* computers, care should be taken to protect from overflow.
-*
-* In the following code, 'long' values have been used for this
-* purpose, instead of 'int'.
-*
-*/
-
-#define DONT_INTERSECT 0
-#define DO_INTERSECT 1
-#define COLLINEAR 2
-
-inline int SAME_SIGNS(double a, double b)
-{
- return ((a>=0 && b>=0) || (a<0 && b<0));
-}
-
-int
-lines_intersect(
-/* 1st line segment */ double x1, double y1, double x2, double y2,
-/* 2nd line segment */ double x3, double y3, double x4, double y4,
-/* pt of intersect */ double& ix, double& iy)
-{
- double a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
- double r1, r2, r3, r4; /* 'Sign' values */
- double denom, offset, num; /* Intermediate values */
-
- /* Compute a1, b1, c1, where line joining points 1 and 2
- * is "a1 x + b1 y + c1 = 0". */
-
- a1 = y2 - y1;
- b1 = x1 - x2;
- c1 = x2 * y1 - x1 * y2;
-
- /* Compute r3 and r4. */
-
- r3 = a1 * x3 + b1 * y3 + c1;
- r4 = a1 * x4 + b1 * y4 + c1;
-
- /* Check signs of r3 and r4. If both point 3 and point 4 lie on
- * same side of line 1, the line segments do not intersect. */
-
- if ( r3 != 0 &&
- r4 != 0 &&
- SAME_SIGNS( r3, r4 ))
- return ( DONT_INTERSECT );
-
- /* Compute a2, b2, c2 */
-
- a2 = y4 - y3;
- b2 = x3 - x4;
- c2 = x4 * y3 - x3 * y4;
-
- /* Compute r1 and r2 */
-
- r1 = a2 * x1 + b2 * y1 + c2;
- r2 = a2 * x2 + b2 * y2 + c2;
-
- /* Check signs of r1 and r2. If both point 1 and point 2 lie
- * on same side of second line segment, the line segments do
- * not intersect. */
-
- if ( r1 != 0 &&
- r2 != 0 &&
- SAME_SIGNS( r1, r2 ))
- return ( DONT_INTERSECT );
-
- /* Line segments intersect: compute intersection point. */
-
- denom = a1 * b2 - a2 * b1;
- if ( denom == 0 )
- return ( DONT_INTERSECT );
- offset = denom < 0 ? - denom / 2 : denom / 2;
-
- /* The denom/2 is to get rounding instead of truncating. It
- * is added or subtracted to the numerator, depending upon the
- * sign of the numerator. */
-
- num = b1 * c2 - b2 * c1;
- ix = ( num < 0 ? num - offset : num + offset ) / denom;
-
- num = a2 * c1 - a1 * c2;
- iy = ( num < 0 ? num - offset : num + offset ) / denom;
-
- return ( DO_INTERSECT );
-}
-
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