X-Git-Url: https://pd.if.org/git/?a=blobdiff_plain;f=hexagon.c;h=2dd1f3a3e5e6094b5633e8ebc93e08d0a6ba8d14;hb=c5a7aa5029146b2bcea5daae53c6aa3e5e33ed04;hp=61bb47b0fd80429ddd49e57df1e72ebb450cfc12;hpb=8ca2b8a06b00066a20f744a61c9bcdd65949a344;p=hexagon

diff --git a/hexagon.c b/hexagon.c
index 61bb47b..2dd1f3a 100644
--- a/hexagon.c
+++ b/hexagon.c
@@ -12,7 +12,7 @@ static int inversecantor(int cantor, int *x, int *y);
  * domain
  */
 
-double HL_vertexv[] = {
+double HL_vertexv[12] = {
 	.577350269189625764509148780502, 0.0,
 	.288675134594812882254574390251, 0.5,
 	-.288675134594812882254574390251, 0.5,
@@ -20,6 +20,54 @@ double HL_vertexv[] = {
 	-.288675134594812882254574390251, -0.5,
 	.288675134594812882254574390251, -0.5};
 
+double HL_fand[16] = {
+	0.0, 0.0,
+	.577350269189625764509148780502, 0.0,
+	.288675134594812882254574390251, 0.5,
+	-.288675134594812882254574390251, 0.5,
+	-.577350269189625764509148780502, 0.0,
+	-.288675134594812882254574390251, -0.5,
+	.288675134594812882254574390251, -0.5,
+	.577350269189625764509148780502, 0.0
+};
+
+double HL_hfand[16] = {
+	0.0, 0.0,
+	0.0, .577350269189625764509148780502,
+	0.5, .288675134594812882254574390251,
+	0.5, -.288675134594812882254574390251,
+	0.0, -.577350269189625764509148780502,
+	-0.5, -.288675134594812882254574390251,
+	-0.5, .288675134594812882254574390251,
+	0.0, .577350269189625764509148780502
+};
+
+float HL_fanf[16] = {
+	0.0f, 0.0f,
+	.577350269189625764509148780502f, 0.0f,
+	.288675134594812882254574390251f, 0.5f,
+	-.288675134594812882254574390251f, 0.5f,
+	-.577350269189625764509148780502f, 0.0f,
+	-.288675134594812882254574390251f, -0.5f,
+	.288675134594812882254574390251f, -0.5f,
+	.577350269189625764509148780502f, 0.0f
+};
+
+float HL_hfanf[16] = {
+	0.0f, 0.0f,
+	0.0f, .577350269189625764509148780502f,
+	0.5f, .288675134594812882254574390251f,
+	0.5f, -.288675134594812882254574390251f,
+	0.0f, -.577350269189625764509148780502f,
+	-0.5f, -.288675134594812882254574390251f,
+	-0.5f, .288675134594812882254574390251f,
+	0.0f, .577350269189625764509148780502f
+};
+
+/* size of a square that will exactly fit in a hexagon */
+/* 2.0/(1+sqrt(3.0)) */
+double HL_square = .73205080756887729352;
+
 /* these all are for a hex one unit across */
 static double          hexptvd[6][2] = {
 	{.577350269189625764509148780502, 0.0},	/* 1.0/sqrt3 */
@@ -53,6 +101,85 @@ static double          hexpthd[6][2] = {
 
 #endif
 
+/*
+c = 1.0 = distance from center to vertex
+b = distance to hex side
+a = distance along hex side
+
+A = angle at point center, this is the polar coord angle
+B = angle from vertex, this is 60 degrees
+C = Other angle, which is 180 - 60 - A = 120 - A
+
+sin B = sin 60 = sqrt(3) / 2
+cos B = cos 60 = 1/2
+
+b = c * sin B / ( sin A cos B + sin B cos A)
+
+c * sin B / ( sin A cos B + sin B cos A)
+
+0.5 * sqrt3
+-------------
+sinA 0.5 + sqrt3 * 0.5 cosA
+
+sqrt3
+-------------
+sinA + sqrt3 cosA
+
+b=
+3
+-------------
+cosA + sqrt3 sinA
+
+x = b cosA
+y = b sinA
+*/
+
+#define RD (180.0 / M_PI)
+/* angle ranges from 0-6 */
+/* distance is 0 at origin, 1.0 at the hex side */
+
+/* return the polar distance ? */
+double HL_polar(double angle, double distance, double *x, double *y) {
+	double A, B, C, b, c;
+	double sinB, sinC;
+#if 0
+	double sqrt3;
+
+	sqrt3 = sqrt(3.0);
+#endif
+
+	/* convert angle to radians */
+	angle = angle * M_PI / 3.0;
+
+	/* calculate the distance along the ray to the hex side */
+
+	A = fmod(angle, M_PI/3.0); /* constrain to within an equilateral */
+	B = M_PI / 3.0;
+	C = M_PI - A - B;
+
+	sinB = sin(B);
+	sinC = sin(C);
+
+	c = 1.0;
+	c = HL_vertexv[0];
+#if 0
+	/* provided for completeness, but we don't use the value */
+	sinA = sin(A);
+	a = c * sinA / sinC;
+#endif
+	b = c * sinB / sinC;
+
+	if (x) {
+		*x = b * cos(angle);
+	}
+	
+	if (y) {
+		*y = b * sin(angle);
+	}
+
+	return b;
+}
+
 void HL_vertices(int cantor, double *vc) {
 	int i;
 	double xc, yc;
@@ -437,14 +564,16 @@ static int hex_iso(struct hex *h) {
 
 #endif
 
+#define COS30 (.866025403784438646763723170752)
+
 int HL_hexbin(double width, double x, double y, int *i, int *j) {
 	double z, rx, ry, rz;
 	double abs_dx, abs_dy, abs_dz;
 	int ix, iy, iz, s;
 	struct hex h;
 
-	/* TODO just hard-code this cosine */
-	x = x / cos(30 * M_PI / 180.0); /* rotated X coord */
+	/*x = x / cos(30 * M_PI / 180.0); */ /* rotated X coord */
+	x = x / COS30;
 	y = y - x / 2.0; /* adjustment for rotated X */
 
 	/* adjust for actual hexwidth */