*
* Vertices in strip are numbered as follows:
*
- * ___ L-2 ___ L-1 ___ 0 ___ 1 ___ 2 ___ 3 ___ 4 __
- * W-1 W-1 0 0 0 0 0
+ * ___ X-2 ___ X-1 ___ 0 ___ 1 ___ 2 ___ 3 ___ 4 __
+ * Y-1 Y-1 0 0 0 0 0
* / \ / \ / \ / \ / \ / \ / \
* / \ / \ / \ / \ / \ / \ / \
- * L-3 ___ L-2 ___ L-1 ___ 0 ___ 1 ___ 2 ___ 3 ___ 4
- * W-2 W-2 W-2 1 1 1 1 1
+ * X-3 ___ X-2 ___ X-1 ___ 0 ___ 1 ___ 2 ___ 3 ___ 4
+ * Y-2 Y-2 Y-2 1 1 1 1 1
* \ / \ / \ / \ / \ / \ / \ /
* \ / \ / \ / \ / \ / \ / \ /
- * ___ L-3 ___ L-2 ___ L-1 ___ 0 ___ 1 ___ 2 ___ 3 __
- * W-3 W-3 W-3 2 2 2 2
+ * ___ X-3 ___ X-2 ___ X-1 ___ 0 ___ 1 ___ 2 ___ 3 __
+ * Y-3 Y-3 Y-3 2 2 2 2
*
* . . . . . . . . . . . . . . .
*
- * L-4 ___ L-3 ___ L-2 ___ L-1 ___ 0 ___ 1 ___ 2 ___ 3
- * 1 1 1 1 W-2 W-2 W-2 W-2
+ * X-4 ___ X-3 ___ X-2 ___ X-1 ___ 0 ___ 1 ___ 2 ___ 3
+ * 1 1 1 1 Y-2 Y-2 Y-2 Y-2
* \ / \ / \ / \ / \ / \ / \ /
* \ / \ / \ / \ / \ / \ / \ /
- * ___ L-4 ___ L-3 ___ L-2 ___ L-1 ___ 0 ___ 1 ___ 2 __
- * 0 0 0 0 W-1 W-1 W-1
+ * ___ X-4 ___ X-3 ___ X-2 ___ X-1 ___ 0 ___ 1 ___ 2 __
+ * 0 0 0 0 Y-1 Y-1 Y-1
*
* Node x,y for
- * 0 <= x < L x = distance along L = length
- * 0 <= y < W y = distance across W = width
+ * 0 <= x < X x = distance along
+ * 0 <= y < Y y = distance across
*
* Vertices are in reading order from diagram above ie x varies fastest.
*
- * W must be even. The actual location opposite (0,0) is (L-(W-1)/2,0),
- * and likewise opposite (0,W-1) is ((W-1)/2,0).
+ * Y must be even. The actual location opposite (0,0) is (X-(Y-1)/2,0),
+ * and likewise opposite (0,Y-1) is ((Y-1)/2,0).
*
* To label edges, we counte anticlockwise[*] from to-the-right:
*
*
* [*] That is, in the direction represented as anticlockwise for
* the vertices (0,*)..(4,*) in the diagram above; and of course
- * that is clockwise for the vertices (L-5,*)..(L-1,*). The
- * numbering has an actual discontinuity between (L-1,*) and (0,*).
+ * that is clockwise for the vertices (X-5,*)..(X-1,*). The
+ * numbering has an actual discontinuity between (X-1,*) and (0,*).
*
* When we iterate over edges, we iterate first over vertices and then
* over edges 0 to 2, disregarding edges 3 to 5.
*/
-#define LN2W 4
-#define L (1<<LN2W)
-#define W 10
-#define N (L*W)
-#define YMASK (~0u << LN2W)
-#define XMASK (~YMASK)
+#define XBITS 4
+#define X (1<<XBITS)
+#define YBITS 4
+#define Y (1<<YBITS)
+
+/* vertex number: 0000 | y | x
+ * YBITS XBITS
+ */
+
+#define N (X*Y)
+#define XMASK (X-1)
+#define YSHIFT XBITS
+#define Y1 (1 << YSHIFT)
+#define YMASK (Y-1 << YSHIFT)
/* Energy has the following parts right now:
*/
* Find R', the `expected' location of R, by
* reflecting S in M (the midpoint of QP).
*
- * Let d = |RR'|
- * m = |PQ|
+ * Let 2d = |RR'|
+ * b = |PQ|
* l = |RS|
*
* Giving energy contribution:
*
* 2
- * m d
+ * b d
* E = F . ----
* vd, edge PQ vd l
*
* S'
* ,'
* ,'
- * R' ,' d" = |SS'| = |RR'| = d
+ * R' ,' 2d" = |SS'| = |RR'| = 2d
* `-._ ,'
- * `-._ ,'
- * ` M
- * ,' `-._
- * ,' `-._
- * ,' ` S
- * ,'
- * ,'
- * R
+ * `-._ ,' By congruent triangles,
+ * ` M with M' = midpoint of RS,
+ * ,' `-._ |MM'| = |RR'|/2 = d
+ * ,' `-._
+ * ,' ` S So use
+ * ,' M' _ , - ' d = |MM'|
+ * ,' _ , - '
+ * R - '
*
* We choose this value for l (rather than |RM|+|MS|, say, or |RM|)
* because we want this symmetry and because we're happy to punish
* avoid being close to R=S.
*/
-static int edge_end2(int v1, int e) {
- if (!(v1 &
+#define V6 6
+
+static int edge_end2(unsigned v1, int e) {
+ /* The topology is equivalent to that of a square lattice with only
+ * half of the diagonals. Ie, the result of shearing the triangular
+ * lattice to make the lines of constant x vertical. This gives
+ * these six directions:
+ *
+ * 2 1
+ * | /
+ * |/
+ * 3--*--0
+ * /|
+ * / |
+ * 4 5
+ *
+ * This also handily makes vertical the numbering discontinuity,
+ * where the join happens.
+ */
+ static const unsigned dx[V6]= { +1, +1, 0, -1, -1, 0 },
+ dy[V6]= { 0, +Y1, +Y1, 0, -Y1, -Y1 };
+ unsigned x, y;
+
+ y= (v1 & YMASK) + dy[e];
+ if (y & ~YMASK) return -1;
- if (e==1 || e==2)
- if (v2 < L)
+ x= (v1 & XMASK) + dx[e];
+ if (x & ~XMASK) {
+ y= (Y-1)*Y1 - y;
+ x &= XMASK;;
+ }
+ return x | y;
+}
+#define D3 3
#define FOR_VERTEX(v) \
for ((v)=0; (v)<N; (v)++)
#define FOR_VPEDGE(v,e) \
- for ((e)=0; (e)<6; (e)++)
+ for ((e)=0; (e)<V6; (e)++)
#define EDGE_END2 edge_end2
#define FOR_VEDGE(v1,e,v2) \
FOR_VPEDGE((v1),(e))
- if (((v2)= EDGE_END2((v1),(e))) >= 0) ; else
+ if (((v2)= EDGE_END2((v1),(e))) < 0) ; else
#define FOR_EDGE(v1,e,v2) \
FOR_VERTEX((v1)) \
FOR_VEDGE((v1),(e),(v2))
-static double energy_function(const double vertices[N][3]) {
- int vertex;
-
- FOR_VERTEX {
-
+#define FOR_COORD(k) \
+ for ((k)=0; (k)<D3; (k)++)
+
+#define K FOR_COORD(k)
+
+static double hypotD(const double p[], const double q[]) {
+ int k;
+ double pq[D3];
+ gsl_vector v;
+
+ K pq[_k]= p[k] - q[k];
+ v.size= D3;
+ v.stride= 1;
+ v.vector.data= pq;
+ /* owner and block ought not to be used */
+
+ return gsl_blas_snrm2(&v);
+}
+
+#ifdef FP_FAST_FMA
+# define ffsqa(factor,term) fma((factor),(factor),(term))
+#else
+# define ffsqu(factor,term) ((factor)*(factor)+(term))
+#endif
+
+static double energy_function(const double vertices[N][D3]) {
+ int pi,e,qi,ri,si, k;
+ double m[D3], mprime[D3], b, d2, l, sigma_bd2_l;
+
+ FOR_EDGE(pi,e,qi) {
+ ri= EDGE_END2(pi,(e+1)%V6); if (r<0) continue;
+ si= EDGE_END2(pi,(e+5)%V6); if (s<0) continue;
+ assert(ri == EDGE_END2(qi,(e+2)%V6));
+ assert(si == EDGE_END2(qi,(e+4)%V6));
+
+ K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5;
+ K mprime[k]= (vertices[ri][k] + vertices[si][k]) * 0.5;
+ b= hypotD(vertices[pi], vertices[qi]);
+ d2= 0; K d2= ffsqa(m[k] - mprime[k], d2);
+ l= hypotD(vertices[ri][k] - vertices[si][k]);
+
+ sigma_bd2_l += b * d2 / l;
+ }
+
+
static gsl_multimin_fminimizer *minimiser;
~ian / moebius2.git / blobdiff