1 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
2 /**
3 * Contains AABB-related code.
4 * \file IceAABB.cpp
5 * \author Pierre Terdiman
6 * \date January, 29, 2000
7 */
8 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
9
10 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
11 /**
12 * AABB class.
13 * \class AABB
14 * \author Pierre Terdiman
15 * \version 1.0
16 */
17 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
18
19 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
20 // Precompiled Header
21 #include "Stdafx.h"
22
23 using namespace IceMaths;
24
25 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
26 /**
27 * Computes the sum of two AABBs.
28 * \param aabb [in] the other AABB
29 * \return Self-Reference
30 */
31 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
Add(const AABB & aabb)32 AABB& AABB::Add(const AABB& aabb)
33 {
34 // Compute new min & max values
35 Point Min; GetMin(Min);
36 Point Tmp; aabb.GetMin(Tmp);
37 Min.Min(Tmp);
38
39 Point Max; GetMax(Max);
40 aabb.GetMax(Tmp);
41 Max.Max(Tmp);
42
43 // Update this
44 SetMinMax(Min, Max);
45 return *this;
46 }
47
48 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
49 /**
50 * Makes a cube from the AABB.
51 * \param cube [out] the cube AABB
52 * \return cube edge length
53 */
54 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
MakeCube(AABB & cube) const55 float AABB::MakeCube(AABB& cube) const
56 {
57 Point Ext; GetExtents(Ext);
58 float Max = Ext.Max();
59
60 Point Cnt; GetCenter(Cnt);
61 cube.SetCenterExtents(Cnt, Point(Max, Max, Max));
62 return Max;
63 }
64
65 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
66 /**
67 * Makes a sphere from the AABB.
68 * \param sphere [out] sphere containing the AABB
69 */
70 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
MakeSphere(Sphere & sphere) const71 void AABB::MakeSphere(Sphere& sphere) const
72 {
73 GetExtents(sphere.mCenter);
74 sphere.mRadius = sphere.mCenter.Magnitude() * 1.00001f; // To make sure sphere::Contains(*this) succeeds
75 GetCenter(sphere.mCenter);
76 }
77
78 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
79 /**
80 * Checks a box is inside another box.
81 * \param box [in] the other AABB
82 * \return true if current box is inside input box
83 */
84 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
IsInside(const AABB & box) const85 bool AABB::IsInside(const AABB& box) const
86 {
87 if(box.GetMin(0)>GetMin(0)) return false;
88 if(box.GetMin(1)>GetMin(1)) return false;
89 if(box.GetMin(2)>GetMin(2)) return false;
90 if(box.GetMax(0)<GetMax(0)) return false;
91 if(box.GetMax(1)<GetMax(1)) return false;
92 if(box.GetMax(2)<GetMax(2)) return false;
93 return true;
94 }
95
96 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
97 /**
98 * Computes the AABB planes.
99 * \param planes [out] 6 planes surrounding the box
100 * \return true if success
101 */
102 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
ComputePlanes(Plane * planes) const103 bool AABB::ComputePlanes(Plane* planes) const
104 {
105 // Checkings
106 if(!planes) return false;
107
108 Point Center, Extents;
109 GetCenter(Center);
110 GetExtents(Extents);
111
112 // Writes normals
113 planes[0].n = Point(1.0f, 0.0f, 0.0f);
114 planes[1].n = Point(-1.0f, 0.0f, 0.0f);
115 planes[2].n = Point(0.0f, 1.0f, 0.0f);
116 planes[3].n = Point(0.0f, -1.0f, 0.0f);
117 planes[4].n = Point(0.0f, 0.0f, 1.0f);
118 planes[5].n = Point(0.0f, 0.0f, -1.0f);
119
120 // Compute a point on each plane
121 Point p0 = Point(Center.x+Extents.x, Center.y, Center.z);
122 Point p1 = Point(Center.x-Extents.x, Center.y, Center.z);
123 Point p2 = Point(Center.x, Center.y+Extents.y, Center.z);
124 Point p3 = Point(Center.x, Center.y-Extents.y, Center.z);
125 Point p4 = Point(Center.x, Center.y, Center.z+Extents.z);
126 Point p5 = Point(Center.x, Center.y, Center.z-Extents.z);
127
128 // Compute d
129 planes[0].d = -(planes[0].n|p0);
130 planes[1].d = -(planes[1].n|p1);
131 planes[2].d = -(planes[2].n|p2);
132 planes[3].d = -(planes[3].n|p3);
133 planes[4].d = -(planes[4].n|p4);
134 planes[5].d = -(planes[5].n|p5);
135
136 return true;
137 }
138
139 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
140 /**
141 * Computes the aabb points.
142 * \param pts [out] 8 box points
143 * \return true if success
144 */
145 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
ComputePoints(Point * pts) const146 bool AABB::ComputePoints(Point* pts) const
147 {
148 // Checkings
149 if(!pts) return false;
150
151 // Get box corners
152 Point min; GetMin(min);
153 Point max; GetMax(max);
154
155 // 7+------+6 0 = ---
156 // /| /| 1 = +--
157 // / | / | 2 = ++-
158 // / 4+---/--+5 3 = -+-
159 // 3+------+2 / y z 4 = --+
160 // | / | / | / 5 = +-+
161 // |/ |/ |/ 6 = +++
162 // 0+------+1 *---x 7 = -++
163
164 // Generate 8 corners of the bbox
165 pts[0] = Point(min.x, min.y, min.z);
166 pts[1] = Point(max.x, min.y, min.z);
167 pts[2] = Point(max.x, max.y, min.z);
168 pts[3] = Point(min.x, max.y, min.z);
169 pts[4] = Point(min.x, min.y, max.z);
170 pts[5] = Point(max.x, min.y, max.z);
171 pts[6] = Point(max.x, max.y, max.z);
172 pts[7] = Point(min.x, max.y, max.z);
173
174 return true;
175 }
176
177 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
178 /**
179 * Gets vertex normals.
180 * \param pts [out] 8 box points
181 * \return true if success
182 */
183 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
GetVertexNormals() const184 const Point* AABB::GetVertexNormals() const
185 {
186 static const float VertexNormals[] =
187 {
188 -INVSQRT3, -INVSQRT3, -INVSQRT3,
189 INVSQRT3, -INVSQRT3, -INVSQRT3,
190 INVSQRT3, INVSQRT3, -INVSQRT3,
191 -INVSQRT3, INVSQRT3, -INVSQRT3,
192 -INVSQRT3, -INVSQRT3, INVSQRT3,
193 INVSQRT3, -INVSQRT3, INVSQRT3,
194 INVSQRT3, INVSQRT3, INVSQRT3,
195 -INVSQRT3, INVSQRT3, INVSQRT3
196 };
197 return (const Point*)VertexNormals;
198 }
199
200 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
201 /**
202 * Returns edges.
203 * \return 24 indices (12 edges) indexing the list returned by ComputePoints()
204 */
205 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
GetEdges() const206 const udword* AABB::GetEdges() const
207 {
208 static const udword Indices[] = {
209 0, 1, 1, 2, 2, 3, 3, 0,
210 7, 6, 6, 5, 5, 4, 4, 7,
211 1, 5, 6, 2,
212 3, 7, 4, 0
213 };
214 return Indices;
215 }
216
217 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
218 /**
219 * Returns edge normals.
220 * \return edge normals in local space
221 */
222 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
GetEdgeNormals() const223 const Point* AABB::GetEdgeNormals() const
224 {
225 static const float EdgeNormals[] =
226 {
227 0, -INVSQRT2, -INVSQRT2, // 0-1
228 INVSQRT2, 0, -INVSQRT2, // 1-2
229 0, INVSQRT2, -INVSQRT2, // 2-3
230 -INVSQRT2, 0, -INVSQRT2, // 3-0
231
232 0, INVSQRT2, INVSQRT2, // 7-6
233 INVSQRT2, 0, INVSQRT2, // 6-5
234 0, -INVSQRT2, INVSQRT2, // 5-4
235 -INVSQRT2, 0, INVSQRT2, // 4-7
236
237 INVSQRT2, -INVSQRT2, 0, // 1-5
238 INVSQRT2, INVSQRT2, 0, // 6-2
239 -INVSQRT2, INVSQRT2, 0, // 3-7
240 -INVSQRT2, -INVSQRT2, 0 // 4-0
241 };
242 return (const Point*)EdgeNormals;
243 }
244
245 // ===========================================================================
246 // (C) 1996-98 Vienna University of Technology
247 // ===========================================================================
248 // NAME: bboxarea
249 // TYPE: c++ code
250 // PROJECT: Bounding Box Area
251 // CONTENT: Computes area of 2D projection of 3D oriented bounding box
252 // VERSION: 1.0
253 // ===========================================================================
254 // AUTHORS: ds Dieter Schmalstieg
255 // ep Erik Pojar
256 // ===========================================================================
257 // HISTORY:
258 //
259 // 19-sep-99 15:23:03 ds last modification
260 // 01-dec-98 15:23:03 ep created
261 // ===========================================================================
262
263 //----------------------------------------------------------------------------
264 // SAMPLE CODE STARTS HERE
265 //----------------------------------------------------------------------------
266
267 // NOTE: This sample program requires OPEN INVENTOR!
268
269 //indexlist: this table stores the 64 possible cases of classification of
270 //the eyepoint with respect to the 6 defining planes of the bbox (2^6=64)
271 //only 26 (3^3-1, where 1 is "inside" cube) of these cases are valid.
272 //the first 6 numbers in each row are the indices of the bbox vertices that
273 //form the outline of which we want to compute the area (counterclockwise
274 //ordering), the 7th entry means the number of vertices in the outline.
275 //there are 6 cases with a single face and and a 4-vertex outline, and
276 //20 cases with 2 or 3 faces and a 6-vertex outline. a value of 0 indicates
277 //an invalid case.
278
279
280 // Original list was made of 7 items, I added an 8th element:
281 // - to padd on a cache line
282 // - to repeat the first entry to avoid modulos
283 //
284 // I also replaced original ints with sbytes.
285
286 static const sbyte gIndexList[64][8] =
287 {
288 {-1,-1,-1,-1,-1,-1,-1, 0}, // 0 inside
289 { 0, 4, 7, 3, 0,-1,-1, 4}, // 1 left
290 { 1, 2, 6, 5, 1,-1,-1, 4}, // 2 right
291 {-1,-1,-1,-1,-1,-1,-1, 0}, // 3 -
292 { 0, 1, 5, 4, 0,-1,-1, 4}, // 4 bottom
293 { 0, 1, 5, 4, 7, 3, 0, 6}, // 5 bottom, left
294 { 0, 1, 2, 6, 5, 4, 0, 6}, // 6 bottom, right
295 {-1,-1,-1,-1,-1,-1,-1, 0}, // 7 -
296 { 2, 3, 7, 6, 2,-1,-1, 4}, // 8 top
297 { 0, 4, 7, 6, 2, 3, 0, 6}, // 9 top, left
298 { 1, 2, 3, 7, 6, 5, 1, 6}, //10 top, right
299 {-1,-1,-1,-1,-1,-1,-1, 0}, //11 -
300 {-1,-1,-1,-1,-1,-1,-1, 0}, //12 -
301 {-1,-1,-1,-1,-1,-1,-1, 0}, //13 -
302 {-1,-1,-1,-1,-1,-1,-1, 0}, //14 -
303 {-1,-1,-1,-1,-1,-1,-1, 0}, //15 -
304 { 0, 3, 2, 1, 0,-1,-1, 4}, //16 front
305 { 0, 4, 7, 3, 2, 1, 0, 6}, //17 front, left
306 { 0, 3, 2, 6, 5, 1, 0, 6}, //18 front, right
307 {-1,-1,-1,-1,-1,-1,-1, 0}, //19 -
308 { 0, 3, 2, 1, 5, 4, 0, 6}, //20 front, bottom
309 { 1, 5, 4, 7, 3, 2, 1, 6}, //21 front, bottom, left
310 { 0, 3, 2, 6, 5, 4, 0, 6}, //22 front, bottom, right
311 {-1,-1,-1,-1,-1,-1,-1, 0}, //23 -
312 { 0, 3, 7, 6, 2, 1, 0, 6}, //24 front, top
313 { 0, 4, 7, 6, 2, 1, 0, 6}, //25 front, top, left
314 { 0, 3, 7, 6, 5, 1, 0, 6}, //26 front, top, right
315 {-1,-1,-1,-1,-1,-1,-1, 0}, //27 -
316 {-1,-1,-1,-1,-1,-1,-1, 0}, //28 -
317 {-1,-1,-1,-1,-1,-1,-1, 0}, //29 -
318 {-1,-1,-1,-1,-1,-1,-1, 0}, //30 -
319 {-1,-1,-1,-1,-1,-1,-1, 0}, //31 -
320 { 4, 5, 6, 7, 4,-1,-1, 4}, //32 back
321 { 0, 4, 5, 6, 7, 3, 0, 6}, //33 back, left
322 { 1, 2, 6, 7, 4, 5, 1, 6}, //34 back, right
323 {-1,-1,-1,-1,-1,-1,-1, 0}, //35 -
324 { 0, 1, 5, 6, 7, 4, 0, 6}, //36 back, bottom
325 { 0, 1, 5, 6, 7, 3, 0, 6}, //37 back, bottom, left
326 { 0, 1, 2, 6, 7, 4, 0, 6}, //38 back, bottom, right
327 {-1,-1,-1,-1,-1,-1,-1, 0}, //39 -
328 { 2, 3, 7, 4, 5, 6, 2, 6}, //40 back, top
329 { 0, 4, 5, 6, 2, 3, 0, 6}, //41 back, top, left
330 { 1, 2, 3, 7, 4, 5, 1, 6}, //42 back, top, right
331 {-1,-1,-1,-1,-1,-1,-1, 0}, //43 invalid
332 {-1,-1,-1,-1,-1,-1,-1, 0}, //44 invalid
333 {-1,-1,-1,-1,-1,-1,-1, 0}, //45 invalid
334 {-1,-1,-1,-1,-1,-1,-1, 0}, //46 invalid
335 {-1,-1,-1,-1,-1,-1,-1, 0}, //47 invalid
336 {-1,-1,-1,-1,-1,-1,-1, 0}, //48 invalid
337 {-1,-1,-1,-1,-1,-1,-1, 0}, //49 invalid
338 {-1,-1,-1,-1,-1,-1,-1, 0}, //50 invalid
339 {-1,-1,-1,-1,-1,-1,-1, 0}, //51 invalid
340 {-1,-1,-1,-1,-1,-1,-1, 0}, //52 invalid
341 {-1,-1,-1,-1,-1,-1,-1, 0}, //53 invalid
342 {-1,-1,-1,-1,-1,-1,-1, 0}, //54 invalid
343 {-1,-1,-1,-1,-1,-1,-1, 0}, //55 invalid
344 {-1,-1,-1,-1,-1,-1,-1, 0}, //56 invalid
345 {-1,-1,-1,-1,-1,-1,-1, 0}, //57 invalid
346 {-1,-1,-1,-1,-1,-1,-1, 0}, //58 invalid
347 {-1,-1,-1,-1,-1,-1,-1, 0}, //59 invalid
348 {-1,-1,-1,-1,-1,-1,-1, 0}, //60 invalid
349 {-1,-1,-1,-1,-1,-1,-1, 0}, //61 invalid
350 {-1,-1,-1,-1,-1,-1,-1, 0}, //62 invalid
351 {-1,-1,-1,-1,-1,-1,-1, 0} //63 invalid
352 };
353
ComputeOutline(const Point & local_eye,sdword & num) const354 const sbyte* AABB::ComputeOutline(const Point& local_eye, sdword& num) const
355 {
356 // Get box corners
357 Point min; GetMin(min);
358 Point max; GetMax(max);
359
360 // Compute 6-bit code to classify eye with respect to the 6 defining planes of the bbox
361 int pos = ((local_eye.x < min.x) ? 1 : 0) // 1 = left
362 + ((local_eye.x > max.x) ? 2 : 0) // 2 = right
363 + ((local_eye.y < min.y) ? 4 : 0) // 4 = bottom
364 + ((local_eye.y > max.y) ? 8 : 0) // 8 = top
365 + ((local_eye.z < min.z) ? 16 : 0) // 16 = front
366 + ((local_eye.z > max.z) ? 32 : 0); // 32 = back
367
368 // Look up number of vertices in outline
369 num = (sdword)gIndexList[pos][7];
370 // Zero indicates invalid case
371 if(!num) return null;
372
373 return &gIndexList[pos][0];
374 }
375
376 // calculateBoxArea: computes the screen-projected 2D area of an oriented 3D bounding box
377
378 //const Point& eye, //eye point (in bbox object coordinates)
379 //const AABB& box, //3d bbox
380 //const Matrix4x4& mat, //free transformation for bbox
381 //float width, float height, int& num)
ComputeBoxArea(const Point & eye,const Matrix4x4 & mat,float width,float height,sdword & num) const382 float AABB::ComputeBoxArea(const Point& eye, const Matrix4x4& mat, float width, float height, sdword& num) const
383 {
384 const sbyte* Outline = ComputeOutline(eye, num);
385 if(!Outline) return -1.0f;
386
387 // Compute box vertices
388 Point vertexBox[8], dst[8];
389 ComputePoints(vertexBox);
390
391 // Transform all outline corners into 2D screen space
392 for(sdword i=0;i<num;i++)
393 {
394 HPoint Projected;
395 vertexBox[Outline[i]].ProjectToScreen(width, height, mat, Projected);
396 dst[i] = Projected;
397 }
398
399 float Sum = (dst[num-1][0] - dst[0][0]) * (dst[num-1][1] + dst[0][1]);
400
401 for(int i=0; i<num-1; i++)
402 Sum += (dst[i][0] - dst[i+1][0]) * (dst[i][1] + dst[i+1][1]);
403
404 return Sum * 0.5f; //return computed value corrected by 0.5
405 }
406