| 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321 |
1×
1×
1×
3×
3×
1×
1×
1×
1×
1×
1×
1×
1×
1×
1×
| import Vector3 from './Vector3';
import glMatrix from '../dep/glmatrix';
var vec3 = glMatrix.vec3;
var EPSILON = 1e-5;
/**
* @constructor
* @alias clay.Ray
* @param {clay.Vector3} [origin]
* @param {clay.Vector3} [direction]
*/
var Ray = function (origin, direction) {
/**
* @type {clay.Vector3}
*/
this.origin = origin || new Vector3();
/**
* @type {clay.Vector3}
*/
this.direction = direction || new Vector3();
};
Ray.prototype = {
constructor: Ray,
// http://www.siggraph.org/education/materials/HyperGraph/raytrace/rayplane_intersection.htm
/**
* Calculate intersection point between ray and a give plane
* @param {clay.Plane} plane
* @param {clay.Vector3} [out]
* @return {clay.Vector3}
*/
intersectPlane: function (plane, out) {
var pn = plane.normal.array;
var d = plane.distance;
var ro = this.origin.array;
var rd = this.direction.array;
var divider = vec3.dot(pn, rd);
// ray is parallel to the plane
if (divider === 0) {
return null;
}
if (!out) {
out = new Vector3();
}
var t = (vec3.dot(pn, ro) - d) / divider;
vec3.scaleAndAdd(out.array, ro, rd, -t);
out._dirty = true;
return out;
},
/**
* Mirror the ray against plane
* @param {clay.Plane} plane
*/
mirrorAgainstPlane: function (plane) {
// Distance to plane
var d = vec3.dot(plane.normal.array, this.direction.array);
vec3.scaleAndAdd(this.direction.array, this.direction.array, plane.normal.array, -d * 2);
this.direction._dirty = true;
},
distanceToPoint: (function () {
var v = vec3.create();
return function (point) {
vec3.sub(v, point, this.origin.array);
// Distance from projection point to origin
var b = vec3.dot(v, this.direction.array);
if (b < 0) {
return vec3.distance(this.origin.array, point);
}
// Squared distance from center to origin
var c2 = vec3.lenSquared(v);
// Squared distance from center to projection point
return Math.sqrt(c2 - b * b);
};
})(),
/**
* Calculate intersection point between ray and sphere
* @param {clay.Vector3} center
* @param {number} radius
* @param {clay.Vector3} out
* @return {clay.Vector3}
*/
intersectSphere: (function () {
var v = vec3.create();
return function (center, radius, out) {
var origin = this.origin.array;
var direction = this.direction.array;
center = center.array;
vec3.sub(v, center, origin);
// Distance from projection point to origin
var b = vec3.dot(v, direction);
// Squared distance from center to origin
var c2 = vec3.squaredLength(v);
// Squared distance from center to projection point
var d2 = c2 - b * b;
var r2 = radius * radius;
// No intersection
if (d2 > r2) {
return;
}
var a = Math.sqrt(r2 - d2);
// First intersect point
var t0 = b - a;
// Second intersect point
var t1 = b + a;
if (!out) {
out = new Vector3();
}
if (t0 < 0) {
if (t1 < 0) {
return null;
}
else {
vec3.scaleAndAdd(out.array, origin, direction, t1);
return out;
}
}
else {
vec3.scaleAndAdd(out.array, origin, direction, t0);
return out;
}
};
})(),
// http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-box-intersection/
/**
* Calculate intersection point between ray and bounding box
* @param {clay.BoundingBox} bbox
* @param {clay.Vector3}
* @return {clay.Vector3}
*/
intersectBoundingBox: function (bbox, out) {
var dir = this.direction.array;
var origin = this.origin.array;
var min = bbox.min.array;
var max = bbox.max.array;
var invdirx = 1 / dir[0];
var invdiry = 1 / dir[1];
var invdirz = 1 / dir[2];
var tmin, tmax, tymin, tymax, tzmin, tzmax;
if (invdirx >= 0) {
tmin = (min[0] - origin[0]) * invdirx;
tmax = (max[0] - origin[0]) * invdirx;
}
else {
tmax = (min[0] - origin[0]) * invdirx;
tmin = (max[0] - origin[0]) * invdirx;
}
if (invdiry >= 0) {
tymin = (min[1] - origin[1]) * invdiry;
tymax = (max[1] - origin[1]) * invdiry;
}
else {
tymax = (min[1] - origin[1]) * invdiry;
tymin = (max[1] - origin[1]) * invdiry;
}
if ((tmin > tymax) || (tymin > tmax)) {
return null;
}
if (tymin > tmin || tmin !== tmin) {
tmin = tymin;
}
if (tymax < tmax || tmax !== tmax) {
tmax = tymax;
}
if (invdirz >= 0) {
tzmin = (min[2] - origin[2]) * invdirz;
tzmax = (max[2] - origin[2]) * invdirz;
}
else {
tzmax = (min[2] - origin[2]) * invdirz;
tzmin = (max[2] - origin[2]) * invdirz;
}
if ((tmin > tzmax) || (tzmin > tmax)) {
return null;
}
if (tzmin > tmin || tmin !== tmin) {
tmin = tzmin;
}
if (tzmax < tmax || tmax !== tmax) {
tmax = tzmax;
}
if (tmax < 0) {
return null;
}
var t = tmin >= 0 ? tmin : tmax;
if (!out) {
out = new Vector3();
}
vec3.scaleAndAdd(out.array, origin, dir, t);
return out;
},
// http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
/**
* Calculate intersection point between ray and three triangle vertices
* @param {clay.Vector3} a
* @param {clay.Vector3} b
* @param {clay.Vector3} c
* @param {boolean} singleSided, CW triangle will be ignored
* @param {clay.Vector3} [out]
* @param {clay.Vector3} [barycenteric] barycentric coords
* @return {clay.Vector3}
*/
intersectTriangle: (function () {
var eBA = vec3.create();
var eCA = vec3.create();
var AO = vec3.create();
var vCross = vec3.create();
return function (a, b, c, singleSided, out, barycenteric) {
var dir = this.direction.array;
var origin = this.origin.array;
a = a.array;
b = b.array;
c = c.array;
vec3.sub(eBA, b, a);
vec3.sub(eCA, c, a);
vec3.cross(vCross, eCA, dir);
var det = vec3.dot(eBA, vCross);
if (singleSided) {
if (det > -EPSILON) {
return null;
}
}
else {
if (det > -EPSILON && det < EPSILON) {
return null;
}
}
vec3.sub(AO, origin, a);
var u = vec3.dot(vCross, AO) / det;
if (u < 0 || u > 1) {
return null;
}
vec3.cross(vCross, eBA, AO);
var v = vec3.dot(dir, vCross) / det;
if (v < 0 || v > 1 || (u + v > 1)) {
return null;
}
vec3.cross(vCross, eBA, eCA);
var t = -vec3.dot(AO, vCross) / det;
if (t < 0) {
return null;
}
if (!out) {
out = new Vector3();
}
if (barycenteric) {
Vector3.set(barycenteric, (1 - u - v), u, v);
}
vec3.scaleAndAdd(out.array, origin, dir, t);
return out;
};
})(),
/**
* Apply an affine transform matrix to the ray
* @return {clay.Matrix4} matrix
*/
applyTransform: function (matrix) {
Vector3.add(this.direction, this.direction, this.origin);
Vector3.transformMat4(this.origin, this.origin, matrix);
Vector3.transformMat4(this.direction, this.direction, matrix);
Vector3.sub(this.direction, this.direction, this.origin);
Vector3.normalize(this.direction, this.direction);
},
/**
* Copy values from another ray
* @param {clay.Ray} ray
*/
copy: function (ray) {
Vector3.copy(this.origin, ray.origin);
Vector3.copy(this.direction, ray.direction);
},
/**
* Clone a new ray
* @return {clay.Ray}
*/
clone: function () {
var ray = new Ray();
ray.copy(this);
return ray;
}
};
export default Ray;
|