wip - add matrix transformations

2023-04-30 15:15:19 -04:00
parent c454ab074a
commit f1dbd714e1
14 changed files with 502 additions and 307 deletions
--- a/helper/matrix.scad
+++ b/helper/matrix.scad
@ -0,0 +1,110 @@
+// Common matrix transformations
+
+identity = [
+    [1,0,0,0],
+    [0,1,0,0],
+    [0,0,1,0],
+    [0,0,0,1],
+  ];
+
+function scale(v) = [
+    [v[0],0,0,0],
+    [0,v[1],0,0],
+    [0,0,v[2],0],
+    [0,0,0,1]
+  ];
+
+function rotatex(a) = [
+    [1,0,0,0],
+    [0,cos(a),-sin(a),0],
+    [0,sin(a),cos(a),0],
+    [0,0,0,1]
+  ];
+
+function rotatey(a) = [
+    [cos(a),0,sin(a),0],
+    [0,1,0,0],
+    [-sin(a),0,cos(a),0],
+    [0,0,0,1]
+  ];
+
+function rotatez(a) = [
+    [cos(a),-sin(a),0,0],
+    [sin(a),cos(a),0,0],
+    [0,0,1,0],
+    [0,0,0,1]
+  ];
+
+function rotate(a,v) =
+  (v == undef)
+  ? rotatez(a[2])*rotatey(a[1])*rotatex(a[0])
+  : rotateanv(a,v/sqrt(v*v));
+
+function translate(v) = [
+    [1,0,0,v[0]],
+    [0,1,0,v[1]],
+    [0,0,1,v[2]],
+    [0,0,0,1]
+  ];
+
+function mirrorabc(a,b,c) = [
+    [1-2*a*a,-2*a*b,-2*a*c,0],
+    [-2*a*b,1-2*b*b,-2*b*c,0],
+    [-2*a*c,-2*b*c,1-2*c*c,0],
+    [0,0,0,1]
+  ];
+
+function mirrornv(nv) = mirrorabc(nv[0],nv[1],nv[2]);
+
+function mirror(v) = mirrornv(v/sqrt(v*v));
+
+
+// taken from https://github.com/openscad/openscad/issues/1040#issuecomment-233208606
+function det4x4(a) =
+a[0][0]*a[1][1]*a[2][2]*a[3][3] + a[0][0]*a[1][2]*a[2][3]*a[3][1] + a[0][0]*a[1][3]*a[2][1]*a[3][2]
+  + a[0][1]*a[1][0]*a[2][3]*a[3][2] + a[0][1]*a[1][2]*a[2][0]*a[3][3] + a[0][1]*a[1][3]*a[2][2]*a[3][0]
+  + a[0][2]*a[1][0]*a[2][1]*a[3][3] + a[0][2]*a[1][1]*a[2][3]*a[3][0] + a[0][2]*a[1][3]*a[2][0]*a[3][1]
+  + a[0][3]*a[1][0]*a[2][2]*a[3][1] + a[0][3]*a[1][1]*a[2][0]*a[3][2] + a[0][3]*a[1][2]*a[2][1]*a[3][0]
+  - a[0][0]*a[1][1]*a[2][3]*a[3][2] - a[0][0]*a[1][2]*a[2][1]*a[3][3] - a[0][0]*a[1][3]*a[2][2]*a[3][1]
+  - a[0][1]*a[1][0]*a[2][2]*a[3][3] - a[0][1]*a[1][2]*a[2][3]*a[3][0] - a[0][1]*a[1][3]*a[2][0]*a[3][2]
+  - a[0][2]*a[1][0]*a[2][3]*a[3][1] - a[0][2]*a[1][1]*a[2][0]*a[3][3] - a[0][2]*a[1][3]*a[2][1]*a[3][0]
+  - a[0][3]*a[1][0]*a[2][1]*a[3][2] - a[0][3]*a[1][1]*a[2][2]*a[3][0] - a[0][3]*a[1][2]*a[2][0]*a[3][1];
+
+function invb00(a) = a[1][1]*a[2][2]*a[3][3] + a[1][2]*a[2][3]*a[3][1] + a[1][3]*a[2][1]*a[3][2] - a[1][1]*a[2][3]*a[3][2] - a[1][2]*a[2][1]*a[3][3] - a[1][3]*a[2][2]*a[3][1];
+
+function invb01(a) = a[0][1]*a[2][3]*a[3][2] + a[0][2]*a[2][1]*a[3][3] + a[0][3]*a[2][2]*a[3][1] - a[0][1]*a[2][2]*a[3][3] - a[0][2]*a[2][3]*a[3][1] - a[0][3]*a[2][1]*a[3][2];
+
+function invb02(a) = a[0][1]*a[1][2]*a[3][3] + a[0][2]*a[1][3]*a[3][1] + a[0][3]*a[1][1]*a[3][2] - a[0][1]*a[1][3]*a[3][2] - a[0][2]*a[1][1]*a[3][3] - a[0][3]*a[1][2]*a[3][1];
+
+function invb03(a) = a[0][1]*a[1][3]*a[2][2] + a[0][2]*a[1][1]*a[2][3] + a[0][3]*a[1][2]*a[2][1] - a[0][1]*a[1][2]*a[2][3] - a[0][2]*a[1][3]*a[2][1] - a[0][3]*a[1][1]*a[2][2];
+
+function invb10(a) = a[1][0]*a[2][3]*a[3][2] + a[1][2]*a[2][0]*a[3][3] + a[1][3]*a[2][2]*a[3][0] - a[1][0]*a[2][2]*a[3][3] - a[1][2]*a[2][3]*a[3][0] - a[1][3]*a[2][0]*a[3][2];
+
+function invb11(a) = a[0][0]*a[2][2]*a[3][3] + a[0][2]*a[2][3]*a[3][0] + a[0][3]*a[2][0]*a[3][2] - a[0][0]*a[2][3]*a[3][2] - a[0][2]*a[2][0]*a[3][3] - a[0][3]*a[2][2]*a[3][0];
+
+function invb12(a) = a[0][0]*a[1][3]*a[3][2] + a[0][2]*a[1][0]*a[3][3] + a[0][3]*a[1][2]*a[3][0] - a[0][0]*a[1][2]*a[3][3] - a[0][2]*a[1][3]*a[3][0] - a[0][3]*a[1][0]*a[3][2];
+
+function invb13(a) = a[0][0]*a[1][2]*a[2][3] + a[0][2]*a[1][3]*a[2][0] + a[0][3]*a[1][0]*a[2][2] - a[0][0]*a[1][3]*a[2][2] - a[0][2]*a[1][0]*a[2][3] - a[0][3]*a[1][2]*a[2][0];
+
+function invb20(a) = a[1][0]*a[2][1]*a[3][3] + a[1][1]*a[2][3]*a[3][0] + a[1][3]*a[2][0]*a[3][1] - a[1][0]*a[2][3]*a[3][1] - a[1][1]*a[2][0]*a[3][3] - a[1][3]*a[2][1]*a[3][0];
+
+function invb21(a) = a[0][0]*a[2][3]*a[3][1] + a[0][1]*a[2][0]*a[3][3] + a[0][3]*a[2][1]*a[3][0] - a[0][0]*a[2][1]*a[3][3] - a[0][1]*a[2][3]*a[3][0] - a[0][3]*a[2][0]*a[3][1];
+
+function invb22(a) = a[0][0]*a[1][1]*a[3][3] + a[0][1]*a[1][3]*a[3][0] + a[0][3]*a[1][0]*a[3][1] - a[0][0]*a[1][3]*a[3][1] - a[0][1]*a[1][0]*a[3][3] - a[0][3]*a[1][1]*a[3][0];
+
+function invb23(a) = a[0][0]*a[1][3]*a[2][1] + a[0][1]*a[1][0]*a[2][3] + a[0][3]*a[1][1]*a[2][0] - a[0][0]*a[1][1]*a[2][3] - a[0][1]*a[1][3]*a[2][0] - a[0][3]*a[1][0]*a[2][1];
+
+function invb30(a) = a[1][0]*a[2][2]*a[3][1] + a[1][1]*a[2][0]*a[3][2] + a[1][2]*a[2][1]*a[3][0] - a[1][0]*a[2][1]*a[3][2] - a[1][1]*a[2][2]*a[3][0] - a[1][2]*a[2][0]*a[3][1];
+
+function invb31(a) = a[0][0]*a[2][1]*a[3][2] + a[0][1]*a[2][2]*a[3][0] + a[0][2]*a[2][0]*a[3][1] - a[0][0]*a[2][2]*a[3][1] - a[0][1]*a[2][0]*a[3][2] - a[0][2]*a[2][1]*a[3][0];
+
+function invb32(a) = a[0][0]*a[1][2]*a[3][1] + a[0][1]*a[1][0]*a[3][2] + a[0][2]*a[1][1]*a[3][0] - a[0][0]*a[1][1]*a[3][2] - a[0][1]*a[1][2]*a[3][0] - a[0][2]*a[1][0]*a[3][1];
+
+function invb33(a) = a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] + a[0][2]*a[1][0]*a[2][1] - a[0][0]*a[1][2]*a[2][1] - a[0][1]*a[1][0]*a[2][2] - a[0][2]*a[1][1]*a[2][0];
+
+function inv4x4(a)= (1/det4x4(a))*[
+    [invb00(a),invb01(a),invb02(a),invb03(a)],
+    [invb10(a),invb11(a),invb12(a),invb13(a)],
+    [invb20(a),invb21(a),invb22(a),invb23(a)],
+    [invb30(a),invb31(a),invb32(a),invb33(a)]];
+