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1///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
2/**
3 * Contains code for 3D vectors.
4 * \file IcePoint.h
5 * \author Pierre Terdiman
6 * \date April, 4, 2000
7 */
8///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
9
10///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
11// Include Guard
12#ifndef __ICEPOINT_H__
13#define __ICEPOINT_H__
14
15 // Forward declarations
16 class HPoint;
17 class Plane;
18 class Matrix3x3;
19 class Matrix4x4;
20
21 #define CROSS2D(a, b) (a.x*b.y - b.x*a.y)
22
23 const float EPSILON2 = 1.0e-20f;
24
25 class ICEMATHS_API Point
26 {
27 public:
28
29 //! Empty constructor
30 inline_ Point() {}
31 //! Constructor from a single float
32// inline_ Point(float val) : x(val), y(val), z(val) {}
33// Removed since it introduced the nasty "Point T = *Matrix4x4.GetTrans();" bug.......
34 //! Constructor from floats
35 inline_ Point(float xx, float yy, float zz) : x(xx), y(yy), z(zz) {}
36 //! Constructor from array
37 inline_ Point(const float f[3]) : x(f[X]), y(f[Y]), z(f[Z]) {}
38 //! Copy constructor
39 inline_ Point(const Point& p) : x(p.x), y(p.y), z(p.z) {}
40 //! Destructor
41 inline_ ~Point() {}
42
43 //! Clears the vector
44 inline_ Point& Zero() { x = y = z = 0.0f; return *this; }
45
46 //! + infinity
47 inline_ Point& SetPlusInfinity() { x = y = z = MAX_FLOAT; return *this; }
48 //! - infinity
49 inline_ Point& SetMinusInfinity() { x = y = z = MIN_FLOAT; return *this; }
50
51 //! Sets positive unit random vector
52 Point& PositiveUnitRandomVector();
53 //! Sets unit random vector
54 Point& UnitRandomVector();
55
56 //! Assignment from values
57 inline_ Point& Set(float xx, float yy, float zz) { x = xx; y = yy; z = zz; return *this; }
58 //! Assignment from array
59 inline_ Point& Set(const float f[3]) { x = f[X]; y = f[Y]; z = f[Z]; return *this; }
60 //! Assignment from another point
61 inline_ Point& Set(const Point& src) { x = src.x; y = src.y; z = src.z; return *this; }
62
63 //! Adds a vector
64 inline_ Point& Add(const Point& p) { x += p.x; y += p.y; z += p.z; return *this; }
65 //! Adds a vector
66 inline_ Point& Add(float xx, float yy, float zz) { x += xx; y += yy; z += zz; return *this; }
67 //! Adds a vector
68 inline_ Point& Add(const float f[3]) { x += f[X]; y += f[Y]; z += f[Z]; return *this; }
69 //! Adds vectors
70 inline_ Point& Add(const Point& p, const Point& q) { x = p.x+q.x; y = p.y+q.y; z = p.z+q.z; return *this; }
71
72 //! Subtracts a vector
73 inline_ Point& Sub(const Point& p) { x -= p.x; y -= p.y; z -= p.z; return *this; }
74 //! Subtracts a vector
75 inline_ Point& Sub(float xx, float yy, float zz) { x -= xx; y -= yy; z -= zz; return *this; }
76 //! Subtracts a vector
77 inline_ Point& Sub(const float f[3]) { x -= f[X]; y -= f[Y]; z -= f[Z]; return *this; }
78 //! Subtracts vectors
79 inline_ Point& Sub(const Point& p, const Point& q) { x = p.x-q.x; y = p.y-q.y; z = p.z-q.z; return *this; }
80
81 //! this = -this
82 inline_ Point& Neg() { x = -x; y = -y; z = -z; return *this; }
83 //! this = -a
84 inline_ Point& Neg(const Point& a) { x = -a.x; y = -a.y; z = -a.z; return *this; }
85
86 //! Multiplies by a scalar
87 inline_ Point& Mult(float s) { x *= s; y *= s; z *= s; return *this; }
88
89 //! this = a * scalar
90 inline_ Point& Mult(const Point& a, float scalar)
91 {
92 x = a.x * scalar;
93 y = a.y * scalar;
94 z = a.z * scalar;
95 return *this;
96 }
97
98 //! this = a + b * scalar
99 inline_ Point& Mac(const Point& a, const Point& b, float scalar)
100 {
101 x = a.x + b.x * scalar;
102 y = a.y + b.y * scalar;
103 z = a.z + b.z * scalar;
104 return *this;
105 }
106
107 //! this = this + a * scalar
108 inline_ Point& Mac(const Point& a, float scalar)
109 {
110 x += a.x * scalar;
111 y += a.y * scalar;
112 z += a.z * scalar;
113 return *this;
114 }
115
116 //! this = a - b * scalar
117 inline_ Point& Msc(const Point& a, const Point& b, float scalar)
118 {
119 x = a.x - b.x * scalar;
120 y = a.y - b.y * scalar;
121 z = a.z - b.z * scalar;
122 return *this;
123 }
124
125 //! this = this - a * scalar
126 inline_ Point& Msc(const Point& a, float scalar)
127 {
128 x -= a.x * scalar;
129 y -= a.y * scalar;
130 z -= a.z * scalar;
131 return *this;
132 }
133
134 //! this = a + b * scalarb + c * scalarc
135 inline_ Point& Mac2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
136 {
137 x = a.x + b.x * scalarb + c.x * scalarc;
138 y = a.y + b.y * scalarb + c.y * scalarc;
139 z = a.z + b.z * scalarb + c.z * scalarc;
140 return *this;
141 }
142
143 //! this = a - b * scalarb - c * scalarc
144 inline_ Point& Msc2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
145 {
146 x = a.x - b.x * scalarb - c.x * scalarc;
147 y = a.y - b.y * scalarb - c.y * scalarc;
148 z = a.z - b.z * scalarb - c.z * scalarc;
149 return *this;
150 }
151
152 //! this = mat * a
153 inline_ Point& Mult(const Matrix3x3& mat, const Point& a);
154
155 //! this = mat1 * a1 + mat2 * a2
156 inline_ Point& Mult2(const Matrix3x3& mat1, const Point& a1, const Matrix3x3& mat2, const Point& a2);
157
158 //! this = this + mat * a
159 inline_ Point& Mac(const Matrix3x3& mat, const Point& a);
160
161 //! this = transpose(mat) * a
162 inline_ Point& TransMult(const Matrix3x3& mat, const Point& a);
163
164 //! Linear interpolate between two vectors: this = a + t * (b - a)
165 inline_ Point& Lerp(const Point& a, const Point& b, float t)
166 {
167 x = a.x + t * (b.x - a.x);
168 y = a.y + t * (b.y - a.y);
169 z = a.z + t * (b.z - a.z);
170 return *this;
171 }
172
173 //! Hermite interpolate between p1 and p2. p0 and p3 are used for finding gradient at p1 and p2.
174 //! this = p0 * (2t^2 - t^3 - t)/2
175 //! + p1 * (3t^3 - 5t^2 + 2)/2
176 //! + p2 * (4t^2 - 3t^3 + t)/2
177 //! + p3 * (t^3 - t^2)/2
178 inline_ Point& Herp(const Point& p0, const Point& p1, const Point& p2, const Point& p3, float t)
179 {
180 float t2 = t * t;
181 float t3 = t2 * t;
182 float kp0 = (2.0f * t2 - t3 - t) * 0.5f;
183 float kp1 = (3.0f * t3 - 5.0f * t2 + 2.0f) * 0.5f;
184 float kp2 = (4.0f * t2 - 3.0f * t3 + t) * 0.5f;
185 float kp3 = (t3 - t2) * 0.5f;
186 x = p0.x * kp0 + p1.x * kp1 + p2.x * kp2 + p3.x * kp3;
187 y = p0.y * kp0 + p1.y * kp1 + p2.y * kp2 + p3.y * kp3;
188 z = p0.z * kp0 + p1.z * kp1 + p2.z * kp2 + p3.z * kp3;
189 return *this;
190 }
191
192 //! this = rotpos * r + linpos
193 inline_ Point& Transform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
194
195 //! this = trans(rotpos) * (r - linpos)
196 inline_ Point& InvTransform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
197
198 //! Returns MIN(x, y, z);
199 inline_ float Min() const { return MIN(x, MIN(y, z)); }
200 //! Returns MAX(x, y, z);
201 inline_ float Max() const { return MAX(x, MAX(y, z)); }
202 //! Sets each element to be componentwise minimum
203 inline_ Point& Min(const Point& p) { x = MIN(x, p.x); y = MIN(y, p.y); z = MIN(z, p.z); return *this; }
204 //! Sets each element to be componentwise maximum
205 inline_ Point& Max(const Point& p) { x = MAX(x, p.x); y = MAX(y, p.y); z = MAX(z, p.z); return *this; }
206
207 //! Clamps each element
208 inline_ Point& Clamp(float min, float max)
209 {
210 if(x<min) x=min; if(x>max) x=max;
211 if(y<min) y=min; if(y>max) y=max;
212 if(z<min) z=min; if(z>max) z=max;
213 return *this;
214 }
215
216 //! Computes square magnitude
217 inline_ float SquareMagnitude() const { return x*x + y*y + z*z; }
218 //! Computes magnitude
219 inline_ float Magnitude() const { return sqrtf(x*x + y*y + z*z); }
220 //! Computes volume
221 inline_ float Volume() const { return x * y * z; }
222
223 //! Checks the point is near zero
224 inline_ bool ApproxZero() const { return SquareMagnitude() < EPSILON2; }
225
226 //! Tests for exact zero vector
227 inline_ BOOL IsZero() const
228 {
229 if(IR(x) || IR(y) || IR(z)) return FALSE;
230 return TRUE;
231 }
232
233 //! Checks point validity
234 inline_ BOOL IsValid() const
235 {
236 if(!IsValidFloat(x)) return FALSE;
237 if(!IsValidFloat(y)) return FALSE;
238 if(!IsValidFloat(z)) return FALSE;
239 return TRUE;
240 }
241
242 //! Slighty moves the point
243 void Tweak(udword coord_mask, udword tweak_mask)
244 {
245 if(coord_mask&1) { udword Dummy = IR(x); Dummy^=tweak_mask; x = FR(Dummy); }
246 if(coord_mask&2) { udword Dummy = IR(y); Dummy^=tweak_mask; y = FR(Dummy); }
247 if(coord_mask&4) { udword Dummy = IR(z); Dummy^=tweak_mask; z = FR(Dummy); }
248 }
249
250 #define TWEAKMASK 0x3fffff
251 #define TWEAKNOTMASK ~TWEAKMASK
252 //! Slighty moves the point out
253 inline_ void TweakBigger()
254 {
255 udword Dummy = (IR(x)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(x)) Dummy+=TWEAKMASK+1; x = FR(Dummy);
256 Dummy = (IR(y)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(y)) Dummy+=TWEAKMASK+1; y = FR(Dummy);
257 Dummy = (IR(z)&TWEAKNOTMASK); if(!IS_NEGATIVE_FLOAT(z)) Dummy+=TWEAKMASK+1; z = FR(Dummy);
258 }
259
260 //! Slighty moves the point in
261 inline_ void TweakSmaller()
262 {
263 udword Dummy = (IR(x)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(x)) Dummy+=TWEAKMASK+1; x = FR(Dummy);
264 Dummy = (IR(y)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(y)) Dummy+=TWEAKMASK+1; y = FR(Dummy);
265 Dummy = (IR(z)&TWEAKNOTMASK); if(IS_NEGATIVE_FLOAT(z)) Dummy+=TWEAKMASK+1; z = FR(Dummy);
266 }
267
268 //! Normalizes the vector
269 inline_ Point& Normalize()
270 {
271 float M = x*x + y*y + z*z;
272 if(M)
273 {
274 M = 1.0f / sqrtf(M);
275 x *= M;
276 y *= M;
277 z *= M;
278 }
279 return *this;
280 }
281
282 //! Sets vector length
283 inline_ Point& SetLength(float length)
284 {
285 float NewLength = length / Magnitude();
286 x *= NewLength;
287 y *= NewLength;
288 z *= NewLength;
289 return *this;
290 }
291
292 //! Clamps vector length
293 inline_ Point& ClampLength(float limit_length)
294 {
295 if(limit_length>=0.0f) // Magnitude must be positive
296 {
297 float CurrentSquareLength = SquareMagnitude();
298
299 if(CurrentSquareLength > limit_length * limit_length)
300 {
301 float Coeff = limit_length / sqrtf(CurrentSquareLength);
302 x *= Coeff;
303 y *= Coeff;
304 z *= Coeff;
305 }
306 }
307 return *this;
308 }
309
310 //! Computes distance to another point
311 inline_ float Distance(const Point& b) const
312 {
313 return sqrtf((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
314 }
315
316 //! Computes square distance to another point
317 inline_ float SquareDistance(const Point& b) const
318 {
319 return ((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
320 }
321
322 //! Dot product dp = this|a
323 inline_ float Dot(const Point& p) const { return p.x * x + p.y * y + p.z * z; }
324
325 //! Cross product this = a x b
326 inline_ Point& Cross(const Point& a, const Point& b)
327 {
328 x = a.y * b.z - a.z * b.y;
329 y = a.z * b.x - a.x * b.z;
330 z = a.x * b.y - a.y * b.x;
331 return *this;
332 }
333
334 //! Vector code ( bitmask = sign(z) | sign(y) | sign(x) )
335 inline_ udword VectorCode() const
336 {
337 return (IR(x)>>31) | ((IR(y)&SIGN_BITMASK)>>30) | ((IR(z)&SIGN_BITMASK)>>29);
338 }
339
340 //! Returns largest axis
341 inline_ PointComponent LargestAxis() const
342 {
343 const float* Vals = &x;
344 PointComponent m = X;
345 if(Vals[Y] > Vals[m]) m = Y;
346 if(Vals[Z] > Vals[m]) m = Z;
347 return m;
348 }
349
350 //! Returns closest axis
351 inline_ PointComponent ClosestAxis() const
352 {
353 const float* Vals = &x;
354 PointComponent m = X;
355 if(AIR(Vals[Y]) > AIR(Vals[m])) m = Y;
356 if(AIR(Vals[Z]) > AIR(Vals[m])) m = Z;
357 return m;
358 }
359
360 //! Returns smallest axis
361 inline_ PointComponent SmallestAxis() const
362 {
363 const float* Vals = &x;
364 PointComponent m = X;
365 if(Vals[Y] < Vals[m]) m = Y;
366 if(Vals[Z] < Vals[m]) m = Z;
367 return m;
368 }
369
370 //! Refracts the point
371 Point& Refract(const Point& eye, const Point& n, float refractindex, Point& refracted);
372
373 //! Projects the point onto a plane
374 Point& ProjectToPlane(const Plane& p);
375
376 //! Projects the point onto the screen
377 void ProjectToScreen(float halfrenderwidth, float halfrenderheight, const Matrix4x4& mat, HPoint& projected) const;
378
379 //! Unfolds the point onto a plane according to edge(a,b)
380 Point& Unfold(Plane& p, Point& a, Point& b);
381
382 //! Hash function from Ville Miettinen
383 inline_ udword GetHashValue() const
384 {
385 const udword* h = (const udword*)(this);
386 udword f = (h[0]+h[1]*11-(h[2]*17)) & 0x7fffffff; // avoid problems with +-0
387 return (f>>22)^(f>>12)^(f);
388 }
389
390 //! Stuff magic values in the point, marking it as explicitely not used.
391 void SetNotUsed();
392 //! Checks the point is marked as not used
393 BOOL IsNotUsed() const;
394
395 // Arithmetic operators
396
397 //! Unary operator for Point Negate = - Point
398 inline_ Point operator-() const { return Point(-x, -y, -z); }
399
400 //! Operator for Point Plus = Point + Point.
401 inline_ Point operator+(const Point& p) const { return Point(x + p.x, y + p.y, z + p.z); }
402 //! Operator for Point Minus = Point - Point.
403 inline_ Point operator-(const Point& p) const { return Point(x - p.x, y - p.y, z - p.z); }
404
405 //! Operator for Point Mul = Point * Point.
406 inline_ Point operator*(const Point& p) const { return Point(x * p.x, y * p.y, z * p.z); }
407 //! Operator for Point Scale = Point * float.
408 inline_ Point operator*(float s) const { return Point(x * s, y * s, z * s ); }
409 //! Operator for Point Scale = float * Point.
410 inline_ friend Point operator*(float s, const Point& p) { return Point(s * p.x, s * p.y, s * p.z); }
411
412 //! Operator for Point Div = Point / Point.
413 inline_ Point operator/(const Point& p) const { return Point(x / p.x, y / p.y, z / p.z); }
414 //! Operator for Point Scale = Point / float.
415 inline_ Point operator/(float s) const { s = 1.0f / s; return Point(x * s, y * s, z * s); }
416 //! Operator for Point Scale = float / Point.
417 inline_ friend Point operator/(float s, const Point& p) { return Point(s / p.x, s / p.y, s / p.z); }
418
419 //! Operator for float DotProd = Point | Point.
420 inline_ float operator|(const Point& p) const { return x*p.x + y*p.y + z*p.z; }
421 //! Operator for Point VecProd = Point ^ Point.
422 inline_ Point operator^(const Point& p) const
423 {
424 return Point(
425 y * p.z - z * p.y,
426 z * p.x - x * p.z,
427 x * p.y - y * p.x );
428 }
429
430 //! Operator for Point += Point.
431 inline_ Point& operator+=(const Point& p) { x += p.x; y += p.y; z += p.z; return *this; }
432 //! Operator for Point += float.
433 inline_ Point& operator+=(float s) { x += s; y += s; z += s; return *this; }
434
435 //! Operator for Point -= Point.
436 inline_ Point& operator-=(const Point& p) { x -= p.x; y -= p.y; z -= p.z; return *this; }
437 //! Operator for Point -= float.
438 inline_ Point& operator-=(float s) { x -= s; y -= s; z -= s; return *this; }
439
440 //! Operator for Point *= Point.
441 inline_ Point& operator*=(const Point& p) { x *= p.x; y *= p.y; z *= p.z; return *this; }
442 //! Operator for Point *= float.
443 inline_ Point& operator*=(float s) { x *= s; y *= s; z *= s; return *this; }
444
445 //! Operator for Point /= Point.
446 inline_ Point& operator/=(const Point& p) { x /= p.x; y /= p.y; z /= p.z; return *this; }
447 //! Operator for Point /= float.
448 inline_ Point& operator/=(float s) { s = 1.0f/s; x *= s; y *= s; z *= s; return *this; }
449
450 // Logical operators
451
452 //! Operator for "if(Point==Point)"
453 inline_ bool operator==(const Point& p) const { return ( (IR(x)==IR(p.x))&&(IR(y)==IR(p.y))&&(IR(z)==IR(p.z))); }
454 //! Operator for "if(Point!=Point)"
455 inline_ bool operator!=(const Point& p) const { return ( (IR(x)!=IR(p.x))||(IR(y)!=IR(p.y))||(IR(z)!=IR(p.z))); }
456
457 // Arithmetic operators
458
459 //! Operator for Point Mul = Point * Matrix3x3.
460 inline_ Point operator*(const Matrix3x3& mat) const
461 {
462 class ShadowMatrix3x3{ public: float m[3][3]; }; // To allow inlining
463 const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
464
465 return Point(
466 x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0],
467 x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1],
468 x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] );
469 }
470
471 //! Operator for Point Mul = Point * Matrix4x4.
472 inline_ Point operator*(const Matrix4x4& mat) const
473 {
474 class ShadowMatrix4x4{ public: float m[4][4]; }; // To allow inlining
475 const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
476
477 return Point(
478 x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0],
479 x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1],
480 x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2]);
481 }
482
483 //! Operator for Point *= Matrix3x3.
484 inline_ Point& operator*=(const Matrix3x3& mat)
485 {
486 class ShadowMatrix3x3{ public: float m[3][3]; }; // To allow inlining
487 const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
488
489 float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0];
490 float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1];
491 float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2];
492
493 x = xp; y = yp; z = zp;
494
495 return *this;
496 }
497
498 //! Operator for Point *= Matrix4x4.
499 inline_ Point& operator*=(const Matrix4x4& mat)
500 {
501 class ShadowMatrix4x4{ public: float m[4][4]; }; // To allow inlining
502 const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
503
504 float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0];
505 float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1];
506 float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2];
507
508 x = xp; y = yp; z = zp;
509
510 return *this;
511 }
512
513 // Cast operators
514
515 //! Cast a Point to a HPoint. w is set to zero.
516 operator HPoint() const;
517
518 inline_ operator const float*() const { return &x; }
519 inline_ operator float*() { return &x; }
520
521 public:
522 float x, y, z;
523 };
524
525 FUNCTION ICEMATHS_API void Normalize1(Point& a);
526 FUNCTION ICEMATHS_API void Normalize2(Point& a);
527
528#endif //__ICEPOINT_H__
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