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26 // 26 //
27 // G4TessellatedGeometryAlgorithms implementat << 27 //
>> 28 //
>> 29 // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> 30 //
>> 31 // CHANGE HISTORY
>> 32 // --------------
28 // 33 //
29 // 07 August 2007, P R Truscott, QinetiQ Ltd, 34 // 07 August 2007, P R Truscott, QinetiQ Ltd, UK - Created, with member
30 // functions based on the work 35 // functions based on the work of Rickard Holmberg.
>> 36 //
>> 37 // 26 September 2007
>> 38 // P R Truscott, qinetiQ Ltd, UK
>> 39 // Updated to assign values of location array, not update
>> 40 // just the pointer.
>> 41 //
31 // 12 October 2012, M Gayer, CERN, - Reviewed 42 // 12 October 2012, M Gayer, CERN, - Reviewed optimized implementation.
32 // ------------------------------------------- << 43 //
>> 44 ///////////////////////////////////////////////////////////////////////////////
33 45
34 #include "G4TessellatedGeometryAlgorithms.hh" 46 #include "G4TessellatedGeometryAlgorithms.hh"
35 47
36 #include <cfloat> 48 #include <cfloat>
37 49
38 ////////////////////////////////////////////// 50 ///////////////////////////////////////////////////////////////////////////////
39 // 51 //
40 // IntersectLineAndTriangle2D 52 // IntersectLineAndTriangle2D
41 // 53 //
42 // Determines whether there is an intersection 54 // Determines whether there is an intersection between a line defined
43 // by r = p + s.v and a triangle defined by ve 55 // by r = p + s.v and a triangle defined by verticies p0, p0+e0 and p0+e1.
44 // 56 //
45 // Here: 57 // Here:
46 // p = 2D vector 58 // p = 2D vector
47 // s = scaler on [0,infinity) 59 // s = scaler on [0,infinity)
48 // v = 2D vector 60 // v = 2D vector
49 // p0, e0 and e1 are 2D vectors 61 // p0, e0 and e1 are 2D vectors
50 // Information about where the intersection oc 62 // Information about where the intersection occurs is returned in the
51 // variable location. 63 // variable location.
52 // 64 //
53 // This is based on the work of Rickard Holmbe 65 // This is based on the work of Rickard Holmberg.
54 // 66 //
55 G4bool G4TessellatedGeometryAlgorithms::Inters 67 G4bool G4TessellatedGeometryAlgorithms::IntersectLineAndTriangle2D (
56 const G4TwoVector& p, const G4TwoVector& v, << 68 const G4TwoVector &p, const G4TwoVector &v,
57 const G4TwoVector& p0, const G4TwoVector& e0 << 69 const G4TwoVector &p0, const G4TwoVector &e0, const G4TwoVector &e1,
58 G4TwoVector location[2]) 70 G4TwoVector location[2])
59 { 71 {
60 G4TwoVector loc0[2]; 72 G4TwoVector loc0[2];
61 G4int e0i = IntersectLineAndLineSegment2D (p 73 G4int e0i = IntersectLineAndLineSegment2D (p,v,p0,e0,loc0);
62 if (e0i == 2) 74 if (e0i == 2)
63 { 75 {
64 location[0] = loc0[0]; 76 location[0] = loc0[0];
65 location[1] = loc0[1]; 77 location[1] = loc0[1];
66 return true; 78 return true;
67 } 79 }
68 80
69 G4TwoVector loc1[2]; 81 G4TwoVector loc1[2];
70 G4int e1i = IntersectLineAndLineSegment2D (p 82 G4int e1i = IntersectLineAndLineSegment2D (p,v,p0,e1,loc1);
71 if (e1i == 2) 83 if (e1i == 2)
72 { 84 {
73 location[0] = loc1[0]; 85 location[0] = loc1[0];
74 location[1] = loc1[1]; 86 location[1] = loc1[1];
75 return true; 87 return true;
76 } 88 }
77 89
78 if ((e0i == 1) && (e1i == 1)) 90 if ((e0i == 1) && (e1i == 1))
79 { 91 {
80 if ((loc0[0]-p).mag2() < (loc1[0]-p).mag2( 92 if ((loc0[0]-p).mag2() < (loc1[0]-p).mag2())
81 { 93 {
82 location[0] = loc0[0]; 94 location[0] = loc0[0];
83 location[1] = loc1[0]; 95 location[1] = loc1[0];
84 } 96 }
85 else 97 else
86 { 98 {
87 location[0] = loc1[0]; 99 location[0] = loc1[0];
88 location[1] = loc0[0]; 100 location[1] = loc0[0];
89 } 101 }
90 return true; 102 return true;
91 } 103 }
92 104
93 G4TwoVector p1 = p0 + e0; 105 G4TwoVector p1 = p0 + e0;
94 G4TwoVector DE = e1 - e0; 106 G4TwoVector DE = e1 - e0;
95 G4TwoVector loc2[2]; 107 G4TwoVector loc2[2];
96 G4int e2i = IntersectLineAndLineSegment2D (p 108 G4int e2i = IntersectLineAndLineSegment2D (p,v,p1,DE,loc2);
97 if (e2i == 2) 109 if (e2i == 2)
98 { 110 {
99 location[0] = loc2[0]; 111 location[0] = loc2[0];
100 location[1] = loc2[1]; 112 location[1] = loc2[1];
101 return true; 113 return true;
102 } 114 }
103 115
104 if ((e0i == 0) && (e1i == 0) && (e2i == 0)) 116 if ((e0i == 0) && (e1i == 0) && (e2i == 0)) return false;
105 117
106 if ((e0i == 1) && (e2i == 1)) 118 if ((e0i == 1) && (e2i == 1))
107 { 119 {
108 if ((loc0[0]-p).mag2() < (loc2[0]-p).mag2( 120 if ((loc0[0]-p).mag2() < (loc2[0]-p).mag2())
109 { 121 {
110 location[0] = loc0[0]; 122 location[0] = loc0[0];
111 location[1] = loc2[0]; 123 location[1] = loc2[0];
112 } 124 }
113 else 125 else
114 { 126 {
115 location[0] = loc2[0]; 127 location[0] = loc2[0];
116 location[1] = loc0[0]; 128 location[1] = loc0[0];
117 } 129 }
118 return true; 130 return true;
119 } 131 }
120 132
121 if ((e1i == 1) && (e2i == 1)) 133 if ((e1i == 1) && (e2i == 1))
122 { 134 {
123 if ((loc1[0]-p).mag2() < (loc2[0]-p).mag2( 135 if ((loc1[0]-p).mag2() < (loc2[0]-p).mag2())
124 { 136 {
125 location[0] = loc1[0]; 137 location[0] = loc1[0];
126 location[1] = loc2[0]; 138 location[1] = loc2[0];
127 } 139 }
128 else 140 else
129 { 141 {
130 location[0] = loc2[0]; 142 location[0] = loc2[0];
131 location[1] = loc1[0]; 143 location[1] = loc1[0];
132 } 144 }
133 return true; 145 return true;
134 } 146 }
135 147
136 return false; 148 return false;
137 } 149 }
138 150
139 ////////////////////////////////////////////// 151 ///////////////////////////////////////////////////////////////////////////////
140 // 152 //
141 // IntersectLineAndLineSegment2D 153 // IntersectLineAndLineSegment2D
142 // 154 //
143 // Determines whether there is an intersection 155 // Determines whether there is an intersection between a line defined
144 // by r = p0 + s.d0 and a line-segment with en 156 // by r = p0 + s.d0 and a line-segment with endpoints p1 and p1+d1.
145 // Here: 157 // Here:
146 // p0 = 2D vector 158 // p0 = 2D vector
147 // s = scaler on [0,infinity) 159 // s = scaler on [0,infinity)
148 // d0 = 2D vector 160 // d0 = 2D vector
149 // p1 and d1 are 2D vectors 161 // p1 and d1 are 2D vectors
150 // 162 //
151 // This function returns: 163 // This function returns:
152 // 0 - if there is no intersection; 164 // 0 - if there is no intersection;
153 // 1 - if there is a unique intersection; 165 // 1 - if there is a unique intersection;
154 // 2 - if the line and line-segments overlap, 166 // 2 - if the line and line-segments overlap, and the intersection is a
155 // segment itself. 167 // segment itself.
156 // Information about where the intersection oc 168 // Information about where the intersection occurs is returned in the
157 // as ??. 169 // as ??.
158 // 170 //
159 // This is based on the work of Rickard Holmbe 171 // This is based on the work of Rickard Holmberg as well as material published
160 // by Philip J Schneider and David H Eberly, " 172 // by Philip J Schneider and David H Eberly, "Geometric Tools for Computer
161 // Graphics," ISBN 1-55860-694-0, pp 244-245, 173 // Graphics," ISBN 1-55860-694-0, pp 244-245, 2003.
162 // 174 //
163 G4int G4TessellatedGeometryAlgorithms::Interse 175 G4int G4TessellatedGeometryAlgorithms::IntersectLineAndLineSegment2D (
164 const G4TwoVector& p0, const G4TwoVector& d0 << 176 const G4TwoVector &p0, const G4TwoVector &d0,
165 const G4TwoVector& p1, const G4TwoVector& d1 << 177 const G4TwoVector &p1, const G4TwoVector &d1,
>> 178 G4TwoVector location[2])
166 { 179 {
167 G4TwoVector e = p1 - p0; 180 G4TwoVector e = p1 - p0;
168 G4double kross = cross(d0,d1); 181 G4double kross = cross(d0,d1);
169 G4double sqrKross = kross * kross; 182 G4double sqrKross = kross * kross;
170 G4double sqrLen0 = d0.mag2(); 183 G4double sqrLen0 = d0.mag2();
171 G4double sqrLen1 = d1.mag2(); 184 G4double sqrLen1 = d1.mag2();
172 location[0] = G4TwoVector(0.0,0.0); 185 location[0] = G4TwoVector(0.0,0.0);
173 location[1] = G4TwoVector(0.0,0.0); 186 location[1] = G4TwoVector(0.0,0.0);
174 187
175 if (sqrKross > DBL_EPSILON * DBL_EPSILON * s 188 if (sqrKross > DBL_EPSILON * DBL_EPSILON * sqrLen0 * sqrLen1)
176 { 189 {
177 // 190 //
178 // The line and line segment are not paral 191 // The line and line segment are not parallel. Determine if the intersection
179 // is in positive s where r=p0 + s*d0, and 192 // is in positive s where r=p0 + s*d0, and for 0<=t<=1 where r=p1 + t*d1.
180 // 193 //
181 G4double ss = cross(e,d1)/kross; 194 G4double ss = cross(e,d1)/kross;
182 if (ss < 0) return 0; // Intersect 195 if (ss < 0) return 0; // Intersection does not occur for positive ss
183 G4double t = cross(e,d0)/kross; 196 G4double t = cross(e,d0)/kross;
184 if (t < 0 || t > 1) return 0; // Intersect 197 if (t < 0 || t > 1) return 0; // Intersection does not occur on line-segment
185 // 198 //
186 // Intersection of lines is a single point 199 // Intersection of lines is a single point on the forward-propagating line
187 // defined by r=p0 + ss*d0, and the line s 200 // defined by r=p0 + ss*d0, and the line segment defined by r=p1 + t*d1.
188 // 201 //
189 location[0] = p0 + ss*d0; 202 location[0] = p0 + ss*d0;
190 return 1; 203 return 1;
191 } 204 }
192 // 205 //
193 // Line and line segment are parallel. Deter 206 // Line and line segment are parallel. Determine whether they overlap or not.
194 // 207 //
195 G4double sqrLenE = e.mag2(); 208 G4double sqrLenE = e.mag2();
196 kross = cross(e,d0); 209 kross = cross(e,d0);
197 sqrKross = kross * kross; 210 sqrKross = kross * kross;
198 if (sqrKross > DBL_EPSILON * DBL_EPSILON * s 211 if (sqrKross > DBL_EPSILON * DBL_EPSILON * sqrLen0 * sqrLenE)
199 { 212 {
200 return 0; //Lines are different. 213 return 0; //Lines are different.
201 } 214 }
202 // 215 //
203 // Lines are the same. Test for overlap. 216 // Lines are the same. Test for overlap.
204 // 217 //
205 G4double s0 = d0.dot(e)/sqrLen0; 218 G4double s0 = d0.dot(e)/sqrLen0;
206 G4double s1 = s0 + d0.dot(d1)/sqrLen0; 219 G4double s1 = s0 + d0.dot(d1)/sqrLen0;
207 G4double smin = 0.0; 220 G4double smin = 0.0;
208 G4double smax = 0.0; 221 G4double smax = 0.0;
209 222
210 if (s0 < s1) {smin = s0; smax = s1;} 223 if (s0 < s1) {smin = s0; smax = s1;}
211 else {smin = s1; smax = s0;} 224 else {smin = s1; smax = s0;}
212 225
213 if (smax < 0.0) return 0; 226 if (smax < 0.0) return 0;
214 else if (smin < 0.0) 227 else if (smin < 0.0)
215 { 228 {
216 location[0] = p0; 229 location[0] = p0;
217 location[1] = p0 + smax*d0; 230 location[1] = p0 + smax*d0;
218 return 2; 231 return 2;
219 } 232 }
220 else 233 else
221 { 234 {
222 location[0] = p0 + smin*d0; 235 location[0] = p0 + smin*d0;
223 location[1] = p0 + smax*d0; 236 location[1] = p0 + smax*d0;
224 return 2; 237 return 2;
225 } 238 }
226 } 239 }
227 240
228 ////////////////////////////////////////////// 241 ///////////////////////////////////////////////////////////////////////////////
229 // 242 //
230 // CrossProduct 243 // CrossProduct
231 // 244 //
232 // This is just a ficticious "cross-product" f 245 // This is just a ficticious "cross-product" function for two 2D vectors...
233 // "ficticious" because such an operation is n 246 // "ficticious" because such an operation is not relevant to 2D space compared
234 // with 3D space. 247 // with 3D space.
235 // 248 //
236 G4double G4TessellatedGeometryAlgorithms::cros << 249 G4double G4TessellatedGeometryAlgorithms::cross(const G4TwoVector &v1,
237 << 250 const G4TwoVector &v2)
238 { 251 {
239 return v1.x()*v2.y() - v1.y()*v2.x(); 252 return v1.x()*v2.y() - v1.y()*v2.x();
240 } 253 }
241 254