diff --git a/beziers.scad b/beziers.scad index e187885..d2aecf0 100644 --- a/beziers.scad +++ b/beziers.scad @@ -927,16 +927,17 @@ function bezier_patch_reverse(patch) = // ptgrid = bezier_patch_points(patch, LIST, LIST); // ptgrid = bezier_patch_points(patch, RANGE, RANGE); // Topics: Bezier Patches -// See Also: bezier_points(), bezier_curve(), bezpath_curve() +// See Also: bezier_patch_normals(), bezier_points(), bezier_curve(), bezpath_curve() // Description: -// Given a square 2-dimensional array of (N+1) by (N+1) points size, that represents a Bezier Patch -// of degree N, returns a point on that surface, at positions `u`, and `v`. A cubic bezier patch -// will be 4x4 points in size. If given a non-square array, each direction will have its own -// degree. +// Sample a bezier patch on a listed point set. The bezier patch must be a rectangular array of +// points, and it will be sampled at all the (u,v) pairs that you specify. If you give u and v +// as single numbers you'll get a single point back. If you give u and v as lists or ranges you'll +// get a 2d rectangular array of points. If one but not both of u and v is a list or range then you'll +// get a list of points. // Arguments: // patch = The 2D array of control points for a Bezier patch. -// u = The proportion of the way along the horizontal inner list of the patch to find the point of. 0<=`u`<=1. If given as a list or range of values, returns a list of point lists. -// v = The proportion of the way along the vertical outer list of the patch to find the point of. 0<=`v`<=1. If given as a list or range of values, returns a list of point lists. +// u = The bezier u parameter (inner list of patch). Generally between 0 and 1. Can be a list, range or value. +// v = The bezier v parameter (outer list of patch). Generally between 0 and 1. Can be a list, range or value. // Example(3D): // patch = [ // [[-50, 50, 0], [-16, 50, 20], [ 16, 50, 20], [50, 50, 0]], @@ -958,15 +959,20 @@ function bezier_patch_reverse(patch) = // pts = bezier_patch_points(patch, [0:0.2:1], [0:0.2:1]); // for (row=pts) move_copies(row) color("magenta") sphere(d=3, $fn=12); function bezier_patch_points(patch, u, v) = - is_num(u) && is_num(v)? bezier_points([for (bez = patch) bezier_points(bez, u)], v) : - assert(is_num(u) || !is_undef(u[0])) - assert(is_num(v) || !is_undef(v[0])) - let( - vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), is_num(u)? [u] : u)] - ) - [for (i = idx(vbezes[0])) bezier_points(column(vbezes,i), is_num(v)? [v] : v)]; + assert(is_range(u) || is_vector(u) || is_finite(u), "Input u is invalid") + assert(is_range(v) || is_vector(v) || is_finite(v), "Input v is invalid") + !is_num(u) && !is_num(v) ? + let( + vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), u)] + ) + [for (i = idx(vbezes[0])) bezier_points(column(vbezes,i), v)] + : is_num(u) && is_num(v)? bezier_points([for (bez = patch) bezier_points(bez, v)], u) + : is_num(u) ? bezier_patch_points(patch,force_list(u),v)[0] + : column(bezier_patch_points(patch,u,force_list(v)),0); + + function _bezier_rectangle(patch, splinesteps=16, style="default") = let( uvals = lerpn(0,1,splinesteps.x+1), @@ -1283,6 +1289,46 @@ function bezier_vnf_degenerate_patch(patch, splinesteps=16, reverse=false, retur ]; +// Function: bezier_patch_normals() +// Usage: +// n = bezier_patch_normals(patch, u, v); +// ngrid = bezier_patch_normals(patch, LIST, LIST); +// ngrid = bezier_patch_normals(patch, RANGE, RANGE); +// Topics: Bezier Patches +// See Also: bezier_patch_points(), bezier_points(), bezier_curve(), bezpath_curve() +// Description: +// Compute the normal vector to a bezier patch at the listed point set. The bezier patch must be a rectangular array of +// points, and the normal will be computed at all the (u,v) pairs that you specify. If you give u and v +// as single numbers you'll get a single point back. If you give u and v as lists or ranges you'll +// get a 2d rectangular array of points. If one but not both of u and v is a list or range then you'll +// get a list of points. +// . +// This function works by computing the cross product of the tangents. If the tangents are parallel, or nearly parallel, the result +// will be invalid. This can happen if you use a degenerate patch, or if you give two of the edges of your patch a smooth corner. +// Arguments: +// patch = The 2D array of control points for a Bezier patch. +// u = The bezier u parameter (inner list of patch). Generally between 0 and 1. Can be a list, range or value. +// v = The bezier v parameter (outer list of patch). Generally between 0 and 1. Can be a list, range or value. +function bezier_patch_normals(patch, u, v) = + assert(is_range(u) || is_vector(u) || is_finite(u), "Input u is invalid") + assert(is_range(v) || is_vector(v) || is_finite(v), "Input v is invalid") + !is_num(u) && !is_num(v) ? + let( + vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), u)], + dvbezes = [for (i = idx(patch[0])) bezier_derivative(column(patch,i), u)], + v_tangent = [for (i = idx(vbezes[0])) bezier_derivative(column(vbezes,i), v)], + u_tangent = [for (i = idx(vbezes[0])) bezier_points(column(dvbezes,i), v)] + ) + [for(i=idx(u_tangent)) [for(j=idx(u_tangent[0])) unit(cross(u_tangent[i][j],v_tangent[i][j]))]] + : is_num(u) && is_num(v)? + let( + du = bezier_derivative([for (bez = patch) bezier_points(bez, v)], u), + dv = bezier_points([for (bez = patch) bezier_derivative(bez, v)], u) + ) + unit(cross(du,dv)) + : is_num(u) ? bezier_patch_normals(patch,force_list(u),v)[0] + : column(bezier_patch_normals(patch,u,force_list(v)),0); + // Section: Debugging Beziers diff --git a/paths.scad b/paths.scad index 35884c7..d19d3ca 100644 --- a/paths.scad +++ b/paths.scad @@ -412,6 +412,7 @@ function subdivide_path(path, n, refine, maxlen, closed=true, exact, method) = let(path = force_path(path)) assert(is_path(path)) assert(num_defined([n,refine,maxlen]),"Must give exactly one of n, refine, and maxlen") + refine==1 || n==len(path) ? path : is_def(maxlen) ? assert(is_undef(method), "Cannot give method with maxlen") assert(is_undef(exact), "Cannot give exact with maxlen")