add polar coordinate calculation

[hexagon] / hexagon.c

diff --git a/hexagon.c b/hexagon.c
index 264734c6c95ee17493d39f0cad5ce411821377da..2dd1f3a3e5e6094b5633e8ebc93e08d0a6ba8d14 100644 (file)
--- a/hexagon.c
+++ b/hexagon.c
@@ -101,6 +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;