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Geometry.h
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1 /* Project nGenEx
2  Destroyer Studios LLC
3  Copyright © 1997-2004. All Rights Reserved.
4 
5  SUBSYSTEM: nGenEx.lib
6  FILE: Geometry.h
7  AUTHOR: John DiCamillo
8 
9 
10  OVERVIEW
11  ========
12  Geometric classes: Rect, Vec3, Point, Matrix, Plane
13 */
14 
15 #ifndef Geometry_h
16 #define Geometry_h
17 
18 #include "Types.h"
19 
20 // +--------------------------------------------------------------------+
21 
22 struct Rect;
23 struct Insets;
24 struct Matrix;
25 struct Vec3;
26 struct Point;
27 struct Quaternion;
28 struct Plane;
29 
30 const double PI = 3.14159265358979323846;
31 const double DEGREES = (PI/180);
32 
33 // +--------------------------------------------------------------------+
34 
35 struct Rect
36 {
37  static const char* TYPENAME() { return "Rect"; }
38 
39  Rect() : x(0), y(0), w(0), h(0) { }
40  Rect(int ix, int iy, int iw, int ih) : x(ix), y(iy), w(iw), h(ih) { }
41 
42  int operator==(const Rect& r) const { return x==r.x && y==r.y && w==r.w && h==r.h; }
43  int operator!=(const Rect& r) const { return x!=r.x || y!=r.y || w!=r.w || h!=r.h; }
44 
45  void Inflate(int dw, int dh);
46  void Deflate(int dw, int dh);
47  void Inset(int left, int right, int top, int bottom);
48  int Contains(int x, int y) const;
49 
50  int x, y, w, h;
51 };
52 
53 // +--------------------------------------------------------------------+
54 
55 struct Insets
56 {
57  Insets() : left(0), right(0), top(0), bottom(0) { }
58  Insets(WORD l, WORD r, WORD t, WORD b) : left(l), right(r), top(t), bottom(b) { }
59 
60  WORD left;
61  WORD right;
62  WORD top;
63  WORD bottom;
64 };
65 
66 // +--------------------------------------------------------------------+
67 
68 struct Matrix
69 {
70  static const char* TYPENAME() { return "Matrix"; }
71 
72  Matrix();
73  Matrix(const Matrix& m);
74  Matrix(const Point& vrt, const Point& vup, const Point& vpn);
75 
76  Matrix& operator = (const Matrix& m);
77  Matrix& operator *= (const Matrix& m);
78 
79  double operator() (int i, int j) const { return elem[i][j]; }
80  double& operator() (int i, int j) { return elem[i][j]; }
81 
82  void Identity();
83  void Transpose();
84  void Rotate(double roll, double pitch, double yaw);
85  void Roll(double roll);
86  void Pitch(double pitch);
87  void Yaw(double yaw);
88  void ComputeEulerAngles(double& roll, double& pitch, double& yaw) const;
89 
90  double Cofactor(int i, int j) const;
91  void Invert();
92 
93  Matrix Inverse() const {
94  Matrix result(*this);
95  result.Invert();
96  return result;
97  }
98 
99  Matrix operator*(const Matrix& m) const;
100  Point operator*(const Point & p) const;
101  Vec3 operator*(const Vec3& v) const;
102 
103  double elem[3][3];
104 
105 private:
106  Matrix(int no_init) { }
107 };
108 
109 // +--------------------------------------------------------------------+
110 
111 struct Vec2
112 {
113  static const char* TYPENAME() { return "Vec2"; }
114 
115  Vec2() { }
116  Vec2(int ix, int iy) : x((float) ix), y((float) iy) { }
117  Vec2(float ix, float iy) : x(ix), y(iy) { }
118  Vec2(double ix, double iy) : x((float) ix), y((float) iy) { }
119 
120  operator void*() const { return (void*) (x || y); }
121  int operator==(const Vec2& p) const { return x==p.x && y==p.y; }
122  int operator!=(const Vec2& p) const { return x!=p.x || y!=p.y; }
123  Vec2 operator+ (const Vec2& p) const { return Vec2(x+p.x, y+p.y); }
124  Vec2 operator- (const Vec2& p) const { return Vec2(x-p.x, y-p.y); }
125  Vec2 operator- () const { return Vec2(-x, -y); }
126  Vec2 operator* (float s) const { return Vec2(x*s, y*s); }
127  Vec2 operator/ (float s) const { return Vec2(x/s, y/s); }
128  float operator*(const Vec2& p) const { return (x*p.x + y*p.y); }
129 
130  Vec2& operator= (const Vec2& p) { x =p.x; y =p.y; return *this; }
131  Vec2& operator+=(const Vec2& p) { x+=p.x; y+=p.y; return *this; }
132  Vec2& operator-=(const Vec2& p) { x-=p.x; y-=p.y; return *this; }
133  Vec2& operator*=(float s) { x*=s; y*=s; return *this; }
134  Vec2& operator/=(float s) { x/=s; y/=s; return *this; }
135 
136  float length() const { return (float) sqrt(x*x+y*y); }
137  float Normalize();
138  float dot(const Vec2& p) const { return (x*p.x + y*p.y); }
139  Vec2 normal() const { return Vec2(-y, x); }
140 
141  float x, y;
142 };
143 
144 // +--------------------------------------------------------------------+
145 
146 struct Vec3
147 {
148  static const char* TYPENAME() { return "Vec3"; }
149 
150  Vec3() { }
151  Vec3(int ix, int iy, int iz) : x((float) ix), y((float) iy), z((float) iz) { }
152  Vec3(float ix, float iy, float iz) : x(ix), y(iy), z(iz) { }
153  Vec3(double ix, double iy, double iz) : x((float) ix), y((float) iy), z((float) iz) { }
154 
155  operator void*() const { return (void*) (x || y || z); }
156  int operator==(const Vec3& p) const { return x==p.x && y==p.y && z==p.z; }
157  int operator!=(const Vec3& p) const { return x!=p.x || y!=p.y || z!=p.z; }
158  Vec3 operator+ (const Vec3& p) const { return Vec3(x+p.x, y+p.y, z+p.z); }
159  Vec3 operator- (const Vec3& p) const { return Vec3(x-p.x, y-p.y, z-p.z); }
160  Vec3 operator- () const { return Vec3(-x, -y, -z); }
161  Vec3 operator* (float s) const { return Vec3(x*s, y*s, z*s); }
162  Vec3 operator/ (float s) const { return Vec3(x/s, y/s, z/s); }
163  float operator* (const Vec3& p) const { return (x*p.x + y*p.y + z*p.z); }
164  Vec3 operator* (const Matrix&) const;
165 
166  Vec3& operator= (const Vec3& p) { x =p.x; y =p.y; z =p.z; return *this; }
167  Vec3& operator+=(const Vec3& p) { x+=p.x; y+=p.y; z+=p.z; return *this; }
168  Vec3& operator-=(const Vec3& p) { x-=p.x; y-=p.y; z-=p.z; return *this; }
169  Vec3& operator*=(float s) { x*=s; y*=s; z*=s; return *this; }
170  Vec3& operator/=(float s) { x/=s; y/=s; z/=s; return *this; }
171 
172  void SwapYZ() { float t = y; y = z; z = t; }
173  float length() const { return (float) sqrt(x*x+y*y+z*z); }
174  float Normalize();
175 
176  float dot(const Vec3& p) const { return (x*p.x + y*p.y + z*p.z); }
177  Vec3 cross(const Vec3& v) const { return Vec3((y*v.z) - (z*v.y),
178  (z*v.x) - (x*v.z),
179  (x*v.y) - (y*v.x)); }
180 
181  float x, y, z;
182 };
183 
184 double ClosestApproachTime(const Vec3& loc1, const Vec3& vel1,
185 const Vec3& loc2, const Vec3& vel2);
186 
187 // +--------------------------------------------------------------------+
188 
189 struct Point
190 {
191  static const char* TYPENAME() { return "Point"; }
192 
193  Point() : x(0), y(0), z(0) { }
194  Point(double ix, double iy, double iz) : x(ix), y(iy), z(iz) { }
195  Point(const Point& p) : x(p.x), y(p.y), z(p.z) { }
196  Point(const Vec3& v) : x(v.x), y(v.y), z(v.z) { }
197 
198  operator Vec3() const { return Vec3((float) x, (float) y, (float) z); }
199 
200  operator void*() const { return (void*) (x || y || z); }
201  int operator==(const Point& p) const { return x==p.x && y==p.y && z==p.z; }
202  int operator!=(const Point& p) const { return x!=p.x || y!=p.y || z!=p.z; }
203  Point operator+ (const Point& p) const { return Point(x+p.x, y+p.y, z+p.z); }
204  Point operator- (const Point& p) const { return Point(x-p.x, y-p.y, z-p.z); }
205  Point operator- () const { return Point(-x, -y, -z); }
206  Point operator* (double s) const { return Point(x*s, y*s, z*s); }
207  Point operator/ (double s) const { return Point(x/s, y/s, z/s); }
208  double operator*(const Point& p) const { return (x*p.x + y*p.y + z*p.z); }
209  Point operator* (const Matrix& m) const;
210 
211  Point& operator= (const Point& p) { x =p.x; y =p.y; z =p.z; return *this; }
212  Point& operator+=(const Point& p) { x+=p.x; y+=p.y; z+=p.z; return *this; }
213  Point& operator-=(const Point& p) { x-=p.x; y-=p.y; z-=p.z; return *this; }
214  Point& operator*=(double s) { x*=s; y*=s; z*=s; return *this; }
215  Point& operator/=(double s) { x/=s; y/=s; z/=s; return *this; }
216 
217  double length() const { return sqrt(x*x+y*y+z*z); }
218  double Normalize();
219  void SwapYZ() { double t = y; y = z; z = t; }
220  Point OtherHand() const { return Point(-x, z, y); }
221 
222  void SetElement(int i, double v);
223 
224  double dot(const Point& p) const { return (x*p.x + y*p.y + z*p.z); }
225  Point cross(const Point& p) const { return Point((y*p.z) - (z*p.y),
226  (z*p.x) - (x*p.z),
227  (x*p.y) - (y*p.x)); }
228 
229  double x, y, z;
230 };
231 
232 double ClosestApproachTime(const Point& loc1, const Point& vel1,
233 const Point& loc2, const Point& vel2);
234 
235 // +--------------------------------------------------------------------+
236 
237 struct Quaternion
238 {
239  static const char* TYPENAME() { return "Quaternion"; }
240 
241  Quaternion() : x(0), y(0), z(0), w(0) { }
242  Quaternion(double ix,
243  double iy,
244  double iz,
245  double iw) : x(ix), y(iy), z(iz), w(iw) { }
246  Quaternion(const Quaternion& q) : x(q.x), y(q.y), z(q.z), w(q.w) { }
247 
248  int operator==(const Quaternion& q) const { return x==q.x && y==q.y && z==q.z && w==q.w; }
249  int operator!=(const Quaternion& q) const { return x!=q.x || y!=q.y || z!=q.z || w!=q.w; }
250 
251  Quaternion operator+ (const Quaternion& q) const { return Quaternion(x+q.x, y+q.y, z+q.z, w+q.w); }
252  Quaternion operator- (const Quaternion& q) const { return Quaternion(x-q.x, y-q.y, z-q.z, w-q.w); }
253  Quaternion operator- () const { return Quaternion(-x, -y, -z, -w); }
254  Quaternion operator* (double s) const { return Quaternion(x*s, y*s, z*s, w*s); }
255  Quaternion operator/ (double s) const { return Quaternion(x/s, y/s, z/s, w/s); }
256 
257  Quaternion& operator= (const Quaternion& q) { x =q.x; y =q.y; z =q.z; w =q.w; return *this; }
258  Quaternion& operator+=(const Quaternion& q) { x+=q.x; y+=q.y; z+=q.z; w+=q.w; return *this; }
259  Quaternion& operator-=(const Quaternion& q) { x-=q.x; y-=q.y; z-=q.z; w-=q.w; return *this; }
260  Quaternion& operator*=(double s) { x*=s; y*=s; z*=s; w*=s; return *this; }
261  Quaternion& operator/=(double s) { x/=s; y/=s; z/=s; w/=s; return *this; }
262 
263  double length() const { return sqrt(x*x + y*y + z*z + w*w); }
264  double Normalize();
265 
266  double x, y, z, w;
267 };
268 
269 // +--------------------------------------------------------------------+
270 
271 struct Plane
272 {
273  static const char* TYPENAME() { return "Plane"; }
274 
275  Plane();
276  Plane(const Point& p0, const Point& p1, const Point& p2);
277  Plane(const Vec3& v0, const Vec3& v1, const Vec3& v2);
278 
279  void Rotate(const Vec3& v0, const Matrix& m);
280  void Translate(const Vec3& v0);
281 
282  float distance;
283  Vec3 normal;
284 };
285 
286 // +--------------------------------------------------------------------+
287 
288 double DotProduct(const Point& a, const Point& b);
289 void CrossProduct(const Point& a, const Point& b, Point& out);
290 void MConcat(double in1[3][3], double in2[3][3], double out[3][3]);
291 
292 // +--------------------------------------------------------------------+
293 
294 int lines_intersect(
295 /* 1st line segment */ double x1, double y1, double x2, double y2,
296 /* 2nd line segment */ double x3, double y3, double x4, double y4,
297 /* intersect point */ double& x, double& y);
298 
299 // +--------------------------------------------------------------------+
300 
301 #endif Geometry_h
302