-// -*- C -*-
-
-function vecdiff2d(a,b) = [b[0]-a[0], b[1]-a[1]];
-function vecdiff(a,b) = [b[0]-a[0], b[1]-a[1], b[2]-a[2]];
-
-#define dsq(i) (a[i]-b[i])*(a[i]-b[i])
-function dist2d(a,b) = sqrt(dsq(0) + dsq(1));
-function dist(a,b) = sqrt(dsq(0) + dsq(1) + dsq(2));
-#undef dsq
-
-#define vsq(i) (v[i]*v[i])
-function vectorlen2d(v) = sqrt(vsq(0) + vsq(1));
-function vectorlen(v) = sqrt(vsq(0) + vsq(1) + vsq(2));
-#undef vsq
-
-function unitvector2d(v) = v / vectorlen2d(v);
-function unitvector(v) = v / vectorlen(v);
-
-function atan2vector(v) = atan2(v[1], v[0]);
-
-// | m[0][0] m[0][1] |
-// | m[1][0] m[1][1] |
-function determinant2(m) = (m[0][0] * m[1][1] - m[0][1] * m[1][0]);
-
-function clockwise2d(v) = [v[1], -v[0]];
-
-function rotate2d(theta, v) = [ v[0] * cos(theta) - v[1] * sin(theta),
- v[1] * cos(theta) + v[0] * sin(theta) ];
-
-// intersection of lines p1..p2 and p3..p4
-function line_intersection_2d(p1,p2,p3,p4) = [
- // from https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Given_two_points_on_each_line
- #define XY12 determinant2([p1,p2])
- #define XY34 determinant2([p3,p4])
- #define XU12 QU(0,1,2)
- #define XU34 QU(0,3,4)
- #define YU12 QU(1,1,2)
- #define YU34 QU(1,3,4)
- #define QU(c,i,j) determinant2([[ p##i[c], 1 ], \
- [ p##j[c], 1 ]])
- #define DENOM \
- determinant2([[ XU12, YU12 ], \
- [ XU34, YU34 ]])
- //----
- determinant2([[ XY12, XU12 ],
- [ XY34, XU34 ]]) / DENOM,
- determinant2([[ XY12, YU12 ],
- [ XY34, YU34 ]]) / DENOM,
- ];
- #undef XY12
- #undef XY34
- #undef XU12
- #undef XU34
- #undef YU12
- #undef YU34
- #undef QU
- #undef DENOM
-
-
-function circle_point(c, r, alpha) = [ c[0] + r * cos(alpha),
- c[1] + r * sin(alpha) ];
-
-#define d (dist2d(a,c))
-#define alpha (atan2(a[1]-c[1],a[0]-c[0]))
-#define gamma (asin(r / d))
-#define beta (alpha + 90 - gamma)
-
-function tangent_intersect_beta(c,r,a) =
- beta;
-
-function tangent_intersect_b(c,r,a) =
- circle_point(c, r, beta);
-#undef d
-#undef alpha
-#undef gamma
-#undef beta
-
-function tangents_intersect_beta(cbig,rbig,csmall,rsmall) =
- tangent_intersect_beta(cbig,rbig-rsmall,csmall);
-
-function reflect_in_y(p) = [-p[0], p[1]];
-
-function angle_map_range(in,base) =
- in < base ? in + 360 :
- in >= base + 360 ? in - 360 :
- in;