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16 * Functions to make faces planar and probably other things.
35 //#include "segment2.h"
40 #define SWAP(a,b) {temp = (a); (a) = (b); (b) = temp;}
42 // -----------------------------------------------------------------------------------------------------------------
43 // Gauss-Jordan elimination solution of a system of linear equations.
44 // a[1..n][1..n] is the input matrix. b[1..n][1..m] is input containing the m right-hand side vectors.
45 // On output, a is replaced by its matrix inverse and b is replaced by the corresponding set of solution vectors.
46 void gaussj(fix **a, int n, fix **b, int m)
48 int indxc[4], indxr[4], ipiv[4];
49 int i, icol=0, irow=0, j, k, l, ll;
50 fix big, dum, pivinv, temp;
53 mprintf((0,"Error -- array too large in gaussj.\n"));
60 for (i=1; i<=n; i++) {
64 for (k=1; k<=n; k++) {
66 if (abs(a[j][k]) >= big) {
71 } else if (ipiv[k] > 1) {
72 mprintf((0,"Error: Singular matrix-1\n"));
79 // We now have the pivot element, so we interchange rows, if needed, to put the pivot
80 // element on the diagonal. The columns are not physically interchanged, only relabeled:
81 // indxc[i], the column of the ith pivot element, is the ith column that is reduced, while
82 // indxr[i] is the row in which that pivot element was originally located. If indxr[i] !=
83 // indxc[i] there is an implied column interchange. With this form of bookkeeping, the
84 // solution b's will end up in the correct order, and the inverse matrix will be scrambled
89 SWAP(a[irow][l], a[icol][l]);
91 SWAP(b[irow][l], b[icol][l]);
96 if (a[icol][icol] == 0) {
97 mprintf((0,"Error: Singular matrix-2\n"));
100 pivinv = fixdiv(F1_0, a[icol][icol]);
101 a[icol][icol] = F1_0;
104 a[icol][l] = fixmul(a[icol][l], pivinv);
106 b[icol][l] = fixmul(b[icol][l], pivinv);
108 for (ll=1; ll<=n; ll++)
113 a[ll][l] -= a[icol][l]*dum;
115 b[ll][l] -= b[icol][l]*dum;
119 // This is the end of the main loop over columns of the reduction. It only remains to unscramble
120 // the solution in view of the column interchanges. We do this by interchanging pairs of
121 // columns in the reverse order that the permutation was built up.
122 for (l=n; l>=1; l--) {
123 if (indxr[l] != indxc[l])
125 SWAP(a[k][indxr[l]], a[k][indxc[l]]);
131 // -----------------------------------------------------------------------------------------------------------------
132 // Return true if side is planar, else return false.
133 int side_is_planar_p(segment *sp, int side)
136 vms_vector *v0,*v1,*v2,*v3;
139 vp = Side_to_verts[side];
140 v0 = &Vertices[sp->verts[vp[0]]];
141 v1 = &Vertices[sp->verts[vp[1]]];
142 v2 = &Vertices[sp->verts[vp[2]]];
143 v3 = &Vertices[sp->verts[vp[3]]];
145 vm_vec_normalize(vm_vec_normal(&va,v0,v1,v2));
146 vm_vec_normalize(vm_vec_normal(&vb,v0,v2,v3));
148 // If the two vectors are very close to being the same, then generate one quad, else generate two triangles.
149 return (vm_vec_dist(&va,&vb) < F1_0/1000);
152 // -------------------------------------------------------------------------------------------------
153 // Return coordinates of a vertex which is vertex v moved so that all sides of which it is a part become planar.
154 void compute_planar_vert(segment *sp, int side, int v, vms_vector *vp)
156 if ((sp) && (side > -3))
160 // -------------------------------------------------------------------------------------------------
161 // Making Cursegp:Curside planar.
162 // If already planar, return.
163 // for each vertex v on side, not part of another segment
164 // choose the vertex v which can be moved to make all sides of which it is a part planar, minimizing distance moved
165 // if there is no vertex v on side, not part of another segment, give up in disgust
167 // 0 curside made planar (or already was)
168 // 1 did not make curside planar
169 int make_curside_planar(void)
173 vms_vector planar_verts[4]; // store coordinates of up to 4 vertices which will make Curside planar, corresponding to each of 4 vertices on side
174 int present_verts[4]; // set to 1 if vertex is present
176 if (side_is_planar_p(Cursegp, Curside))
179 // Look at all vertices in side to find a free one.
181 present_verts[v] = 0;
183 vp = Side_to_verts[Curside];
185 for (v=0; v<4; v++) {
186 int v1 = vp[v]; // absolute vertex id
187 if (is_free_vertex(Cursegp->verts[v1])) {
188 compute_planar_vert(Cursegp, Curside, Cursegp->verts[v1], &planar_verts[v]);
189 present_verts[v] = 1;
193 // Now, for each v for which present_verts[v] == 1, there is a vector (point) in planar_verts[v].
194 // See which one is closest to the plane defined by the other three points.
195 // Nah...just use the first one we find.
197 if (present_verts[v]) {
198 med_set_vertex(vp[v],&planar_verts[v]);
199 validate_segment(Cursegp);
200 // -- should propagate tmaps to segments or something here...
204 // We tried, but we failed, to make Curside planer.