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