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Revar Desmera
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5c4032f054
2 changed files with 61 additions and 14 deletions
74
beziers.scad
74
beziers.scad
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@ -927,16 +927,17 @@ function bezier_patch_reverse(patch) =
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// ptgrid = bezier_patch_points(patch, LIST, LIST);
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// ptgrid = bezier_patch_points(patch, RANGE, RANGE);
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// Topics: Bezier Patches
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// See Also: bezier_points(), bezier_curve(), bezpath_curve()
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// See Also: bezier_patch_normals(), bezier_points(), bezier_curve(), bezpath_curve()
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// Description:
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// Given a square 2-dimensional array of (N+1) by (N+1) points size, that represents a Bezier Patch
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// of degree N, returns a point on that surface, at positions `u`, and `v`. A cubic bezier patch
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// will be 4x4 points in size. If given a non-square array, each direction will have its own
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// degree.
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// Sample a bezier patch on a listed point set. The bezier patch must be a rectangular array of
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// points, and it will be sampled at all the (u,v) pairs that you specify. If you give u and v
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// as single numbers you'll get a single point back. If you give u and v as lists or ranges you'll
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// get a 2d rectangular array of points. If one but not both of u and v is a list or range then you'll
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// get a list of points.
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// Arguments:
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// patch = The 2D array of control points for a Bezier patch.
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// 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.
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// 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.
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// u = The bezier u parameter (inner list of patch). Generally between 0 and 1. Can be a list, range or value.
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// v = The bezier v parameter (outer list of patch). Generally between 0 and 1. Can be a list, range or value.
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// Example(3D):
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// patch = [
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// [[-50, 50, 0], [-16, 50, 20], [ 16, 50, 20], [50, 50, 0]],
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@ -958,15 +959,20 @@ function bezier_patch_reverse(patch) =
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// pts = bezier_patch_points(patch, [0:0.2:1], [0:0.2:1]);
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// for (row=pts) move_copies(row) color("magenta") sphere(d=3, $fn=12);
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function bezier_patch_points(patch, u, v) =
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is_num(u) && is_num(v)? bezier_points([for (bez = patch) bezier_points(bez, u)], v) :
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assert(is_num(u) || !is_undef(u[0]))
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assert(is_num(v) || !is_undef(v[0]))
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let(
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vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), is_num(u)? [u] : u)]
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)
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[for (i = idx(vbezes[0])) bezier_points(column(vbezes,i), is_num(v)? [v] : v)];
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assert(is_range(u) || is_vector(u) || is_finite(u), "Input u is invalid")
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assert(is_range(v) || is_vector(v) || is_finite(v), "Input v is invalid")
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!is_num(u) && !is_num(v) ?
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let(
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vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), u)]
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)
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[for (i = idx(vbezes[0])) bezier_points(column(vbezes,i), v)]
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: is_num(u) && is_num(v)? bezier_points([for (bez = patch) bezier_points(bez, v)], u)
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: is_num(u) ? bezier_patch_points(patch,force_list(u),v)[0]
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: column(bezier_patch_points(patch,u,force_list(v)),0);
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function _bezier_rectangle(patch, splinesteps=16, style="default") =
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let(
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uvals = lerpn(0,1,splinesteps.x+1),
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@ -1283,6 +1289,46 @@ function bezier_vnf_degenerate_patch(patch, splinesteps=16, reverse=false, retur
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];
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// Function: bezier_patch_normals()
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// Usage:
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// n = bezier_patch_normals(patch, u, v);
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// ngrid = bezier_patch_normals(patch, LIST, LIST);
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// ngrid = bezier_patch_normals(patch, RANGE, RANGE);
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// Topics: Bezier Patches
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// See Also: bezier_patch_points(), bezier_points(), bezier_curve(), bezpath_curve()
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// Description:
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// Compute the normal vector to a bezier patch at the listed point set. The bezier patch must be a rectangular array of
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// points, and the normal will be computed at all the (u,v) pairs that you specify. If you give u and v
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// as single numbers you'll get a single point back. If you give u and v as lists or ranges you'll
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// get a 2d rectangular array of points. If one but not both of u and v is a list or range then you'll
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// get a list of points.
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// .
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// This function works by computing the cross product of the tangents. If the tangents are parallel, or nearly parallel, the result
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// 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.
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// Arguments:
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// patch = The 2D array of control points for a Bezier patch.
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// u = The bezier u parameter (inner list of patch). Generally between 0 and 1. Can be a list, range or value.
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// v = The bezier v parameter (outer list of patch). Generally between 0 and 1. Can be a list, range or value.
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function bezier_patch_normals(patch, u, v) =
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assert(is_range(u) || is_vector(u) || is_finite(u), "Input u is invalid")
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assert(is_range(v) || is_vector(v) || is_finite(v), "Input v is invalid")
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!is_num(u) && !is_num(v) ?
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let(
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vbezes = [for (i = idx(patch[0])) bezier_points(column(patch,i), u)],
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dvbezes = [for (i = idx(patch[0])) bezier_derivative(column(patch,i), u)],
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v_tangent = [for (i = idx(vbezes[0])) bezier_derivative(column(vbezes,i), v)],
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u_tangent = [for (i = idx(vbezes[0])) bezier_points(column(dvbezes,i), v)]
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)
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[for(i=idx(u_tangent)) [for(j=idx(u_tangent[0])) unit(cross(u_tangent[i][j],v_tangent[i][j]))]]
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: is_num(u) && is_num(v)?
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let(
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du = bezier_derivative([for (bez = patch) bezier_points(bez, v)], u),
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dv = bezier_points([for (bez = patch) bezier_derivative(bez, v)], u)
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)
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unit(cross(du,dv))
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: is_num(u) ? bezier_patch_normals(patch,force_list(u),v)[0]
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: column(bezier_patch_normals(patch,u,force_list(v)),0);
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// Section: Debugging Beziers
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@ -412,6 +412,7 @@ function subdivide_path(path, n, refine, maxlen, closed=true, exact, method) =
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let(path = force_path(path))
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assert(is_path(path))
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assert(num_defined([n,refine,maxlen]),"Must give exactly one of n, refine, and maxlen")
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refine==1 || n==len(path) ? path :
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is_def(maxlen) ?
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assert(is_undef(method), "Cannot give method with maxlen")
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assert(is_undef(exact), "Cannot give exact with maxlen")
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