discovered De Castlejau's algorithm

The recusion prevents the need for using the Bernstein polynomial.

2 files changed, 21 insertions, 18 deletions

diff --git a/chess/bezier.scad b/chess/bezier.scad
index 4a75cb6..4566d71 100644
--- a/chess/bezier.scad
+++ b/chess/bezier.scad
@@ -30,17 +30,27 @@ function bezier_p0(point, degree, index, t) =
 	binomial_coefficient(degree, index) * ((1 - t) ^ (degree - index)) * (t ^ index) * point;
 
 function bezier_p(points, t) =
-	[for (i=[1:len(points[0])]) sum(bezier_p0(points[i], len(points) - 1, i, t))];
+	[for (i=[1:len(points)-1]) sum(bezier_p0(points[i], len(points)-1, i, t))];
 		
 function bezier_p_debug(points, t) =
-	[for (i=[1:len(points[0])]) sum(bezier_p0(points[i], len(points) - 1, i, t))];
+	[for (i=[1:len(points)-2]) sum(bezier_p0(points[i], len(points)+1, i, t))];
 		
+function de_casteljau(points, t) = 
+    len(points) == 1 ?
+	points[0] : 
+    de_casteljau(
+		[for (i = [0:len(points)-2]) (1 - t) * points[i] + t * points[i + 1]], 
+		t
+	) ;
+
+function bezier_curve(points, $fn=$fn) = 
+    [for (i = [0:$fn]) de_casteljau(points, i / $fn)] ;
+
 p0 = [0, 0];
 p1 = [10, 0];
 pb = [1, 5];
 pn = [0, 10];
 
-
 points = $fn;
 
 points_list = [for (i=[0:points]) bezier_3(p0, p1, pn, i/points)];
@@ -57,9 +67,9 @@ translate([20, 0, 0])
 p_set_1 = [p0, p1, pn];
 p_set_2 = [p0, p1, pb, pn];
 
-points_list_p1 = [for (i=[0:$fn]) bezier_p(p_set_1, i/$fn)];
+points_list_p1 = bezier_curve(p_set_1);
 points_list_p2 = [for (i=[0:$fn]) bezier_p(p_set_2, i/$fn)];
-points_list_p2d = [for (i=[0:$fn]) bezier_p_debug(p_set_2, i/$fn)];
+points_list_p2d = bezier_curve(p_set_2);
 
 for (i=[0:$fn]) {
 	echo("i", i, bezier_p(p_set_2, i/$fn));
diff --git a/chess/demo.scad b/chess/demo.scad
index 7820f67..ec80514 100644
--- a/chess/demo.scad
+++ b/chess/demo.scad
@@ -3,19 +3,12 @@ function bezier(points, t) =
     bezier([for (i = [0:len(points)-2]) 
         (1 - t) * points[i] + t * points[i + 1]], t);
 
-function bezier_curve(points, steps) = 
-    [for (i = [0:steps]) bezier(points, i / steps)];
+function bezier_curve(points, $fn=$fn) = 
+    [for (i = [0:$fn]) bezier(points, i / $fn)];
 
-points = [[0, 0], [10, 0], [1, 5], [0, 10]];
-steps = 100;
-curve = bezier_curve(points, steps);
+points = [[0, 0], [10, 0], [1, 5], [20, 1], [0, 10]];
+$fn = 100;
+	
+curve = bezier_curve(points);
 
 polygon(curve);
-
-// alt
-
-points2 = [[0, 0, 0], [10, 0, 5], [1, 5, 10], [0, 10, 15]];
-// steps = 100;
-curve2 = bezier_curve(points2, steps);
-
-polyhedron(points=curve2, faces=[[for (i=[0:len(curve2)-2]) [i, i+1]]]);