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doc tweaks
fix interface to bezier_curve()
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Adrian Mariano
parent
b41b90bc2a
commit
c93f2041dc
2 changed files with 34 additions and 30 deletions
62
beziers.scad
62
beziers.scad
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@ -40,7 +40,7 @@
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// is best when `u` is a long list and the bezier degree is 10 or less. The degree of the bezier
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// curve is `len(bezier)-1`.
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// Arguments:
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// bezier = The list of endpoints and control points for this bezier segment.
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// bezier = The list of endpoints and control points for this bezier curve.
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// u = Parameter values for evaluating the curve, given as a single value, a list or a range.
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// Example(2D): Quadratic (Degree 2) Bezier.
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// bez = [[0,0], [30,30], [80,0]];
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@ -177,20 +177,21 @@ function _bezier_matrix(N) =
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// Function: bezier_curve()
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// Usage:
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// path = bezier_curve(bezier, n, [endpoint]);
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// path = bezier_curve(bezier, [splinesteps], [endpoint]);
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// Topics: Bezier Curves
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// See Also: bezier_curvature(), bezier_tangent(), bezier_derivative(), bezier_points()
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// Description:
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// Takes a list of bezier control points and generates n points along the bezier curve they define.
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// Takes a list of bezier control points and generates splinesteps segments (splinesteps+1 points)
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// along the bezier curve they define.
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// Points start at the first control point and are sampled uniformly along the bezier parameter.
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// The endpoints of the output will be *exactly* equal to the first and last bezier control points
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// when endpoint is true. If endpoint is false the sampling stops one step before the final point
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// of the bezier curve, but you still get n, more tightly spaced, points.
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// of the bezier curve, but you still get the same number of (more tightly spaced) points.
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// The distance between the points will *not* be equidistant.
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// The degree of the bezier curve is one less than the number of points in `curve`.
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// Arguments:
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// bezier = The list of control points that define the Bezier curve.
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// n = The number of points to generate along the bezier curve.
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// splinesteps = The number of segments to create on the bezier curve. Default: 16
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// endpoint = if false then exclude the endpoint. Default: True
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// Example(2D): Quadratic (Degree 2) Bezier.
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// bez = [[0,0], [30,30], [80,0]];
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@ -204,8 +205,8 @@ function _bezier_matrix(N) =
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// bez = [[0,0], [5,15], [40,20], [60,-15], [80,0]];
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// move_copies(bezier_curve(bez, 8)) sphere(r=1.5, $fn=12);
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// debug_bezier(bez, N=len(bez)-1);
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function bezier_curve(bezier,n,endpoint=true) =
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bezier_points(bezier, lerpn(0,1,n,endpoint));
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function bezier_curve(bezier,splinesteps=16,endpoint=true) =
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bezier_points(bezier, lerpn(0,1,splinesteps+1,endpoint));
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// Function: bezier_derivative()
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@ -288,9 +289,9 @@ function bezier_curvature(bezier, u) =
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// Topics: Bezier Curves
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// See Also: bezier_points()
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// Description:
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// Finds the closest part of the given bezier segment to point `pt`.
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// Finds the closest part of the given bezier curve to point `pt`.
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// The degree of the curve, N, is one less than the number of points in `curve`.
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// Returns `u` for the shortest position on the bezier segment to the given point `pt`.
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// Returns `u` for the closest position on the bezier curve to the given point `pt`.
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// Arguments:
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// bezier = The list of control points that define the Bezier curve.
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// pt = The point to find the closest curve point to.
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@ -401,22 +402,25 @@ function bezier_line_intersection(bezier, line) =
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// Bezier curve control point set is `[p0,p1,p2,p3]` and the second one is `[p3,p4,p5,p6]`. The endpoint, `p3`, is shared between the control point sets.
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// The Bezier degree, which must be known to interpret the Bezier path, defaults to 3.
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// Function: bezpath_points()
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// Usage:
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// pt = bezpath_points(bezpath, seg, u, [N]);
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// ptlist = bezpath_points(bezpath, seg, LIST, [N]);
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// path = bezpath_path_points(bezpath, seg, RANGE, [N]);
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// pt = bezpath_points(bezpath, curveind, u, [N]);
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// ptlist = bezpath_points(bezpath, curveind, LIST, [N]);
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// path = bezpath_points(bezpath, curveind, RANGE, [N]);
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// Topics: Bezier Paths
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// See Also: bezier_points(), bezier_curve()
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// Description:
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// Returns the coordinates of Bezier path path segment `seg` at parameter `u`.
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// Extracts from the Bezier path `bezpath` the control points for the Bezier curve whose index is `curveind` and
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// computes the point or points on the corresponding Bezier curve specified by `u`. If `curveind` is zero you
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// get the first curve. The number of curves is `(len(bezpath)-1)/N` so the maximum index is that number minus one.
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// Arguments:
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// path = A Bezier path path to approximate.
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// seg = Segment number along the path. Each segment is N points long.
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// bezpath = A Bezier path path to approximate.
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// curveind = Curve number along the path.
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// u = Parameter values for evaluating the curve, given as a single value, a list or a range.
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// N = The degree of the Bezier path curves. Cubic Bezier paths have N=3. Default: 3
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function bezpath_points(bezpath, seg, u, N=3) =
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bezier_points(select(bezpath,seg*N,(seg+1)*N), u);
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// N = The degree of the Bezier path curves. Default: 3
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function bezpath_points(bezpath, curveind, u, N=3) =
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bezier_points(select(bezpath,curveind*N,(curveind+1)*N), u);
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// Function: bezpath_curve()
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@ -428,7 +432,7 @@ function bezpath_points(bezpath, seg, u, N=3) =
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// Takes a bezier path and converts it into a path of points.
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// Arguments:
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// bezpath = A bezier path to approximate.
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// splinesteps = Number of straight lines to split each bezier segment into. default=16
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// splinesteps = Number of straight lines to split each bezier curve into. default=16
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// N = The degree of the bezier curves. Cubic beziers have N=3. Default: 3
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// endpoint = If true, include the very last point of the bezier path. Default: true
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// Example(2D):
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@ -975,16 +979,15 @@ function _bezier_rectangle(patch, splinesteps=16, style="default") =
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// Topics: Bezier Patches
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// See Also: bezier_patch_points(), bezier_patch_flat()
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// Description:
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// Calculate vertices and faces for forming a (possibly partial) polyhedron from the given
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// bezier patch or list of patches. Returns a [VNF structure](vnf.scad): a list
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// containing two elements. The first is the the list of vertices. The second is the list
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// of faces, where each face is a list of indices into the list of vertices. The splinesteps argument specifies
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// the number of segments on the borders of the patch or patches. It can be a scalar or
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// it can be [XSTEPS, YSTEPS]. Note that the surface you produce maybe
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// disconnected and is not necessarily a valid polyhedron.
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// Convert a patch or list of patches into the corresponding Bezier surface, representing the
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// result as a [VNF structure](vnf.scad). The `splinesteps` argument specifies the sampling grid of
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// the surface for each patch by specifying the number of segments on the borders of the surface.
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// It can be a scalar, which gives a uniform grid, or
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// it can be [USTEPS, VSTEPS], which gives difference spacing in the U and V parameters.
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// Note that the surface you produce may be disconnected and is not necessarily a valid manifold in OpenSCAD.
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// Arguments:
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// patches = The bezier patch or list of bezier patches to convert into a surface.
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// splinesteps = Number of steps to divide each bezier segment into. For rectangular patches you can specify [XSTEPS,YSTEPS]. Default: 16
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// patches = The bezier patch or list of bezier patches to convert into a vnf.
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// splinesteps = Number of segments on the border of the bezier surface. You can specify [USTEPS,VSTEPS]. Default: 16
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// style = The style of subdividing the quads into faces. Valid options are "default", "alt", "min_edge", "quincunx", "convex" and "concave". See {{vnf_vertex_array()}}. Default: "default"
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// Example(3D):
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// patch = [
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@ -1343,7 +1346,7 @@ module debug_bezier(bezpath, width=1, N=3) {
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// Arguments:
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// patches = A list of rectangular bezier patches.
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// ---
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// splinesteps = Number of steps to divide each bezier segment into. default=16
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// splinesteps = Number of segments to divide each bezier curve into. Default: 16
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// showcps = If true, show the controlpoints as well as the surface. Default: true.
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// showdots = If true, shows the calculated surface vertices. Default: false.
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// showpatch = If true, shows the surface faces. Default: true.
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@ -1383,6 +1386,7 @@ module debug_bezier_patches(patches=[], size, splinesteps=16, showcps=true, show
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for (i=[0:1:len(patch)-1], j=[0:1:len(patch[i])-1]) {
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if (i<len(patch)-1) extrude_from_to(patch[i][j], patch[i+1][j]) circle(d=size);
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if (j<len(patch[i])-1) extrude_from_to(patch[i][j], patch[i][j+1]) circle(d=size);
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}
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}
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if (showpatch || showdots){
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vnf = bezier_vnf(patch, splinesteps=splinesteps, style=style);
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@ -347,7 +347,7 @@ function _bezcorner(points, parm) =
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] : _smooth_bez_fill(points,parm),
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N = max(3,$fn>0 ?$fn : ceil(bezier_length(P)/$fs))
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)
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bezier_curve(P,N+1,endpoint=true);
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bezier_curve(P,N,endpoint=true);
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function _chamfcorner(points, parm) =
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let(
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