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Added Synopses to beziers.scad

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Revar Desmera 2023-04-03 19:22:51 -07:00
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@ -28,11 +28,13 @@
// Section: Bezier Curves // Section: Bezier Curves
// Function: bezier_points() // Function: bezier_points()
// Synopsis: Computes one or more specified points along a bezier curve.
// Topics: Bezier Curves
// See Also: bezier_curve(), bezier_curvature(), bezier_tangent(), bezier_derivative(), bezier_points()
// Usage: // Usage:
// pt = bezier_points(bezier, u); // pt = bezier_points(bezier, u);
// ptlist = bezier_points(bezier, RANGE); // ptlist = bezier_points(bezier, RANGE);
// ptlist = bezier_points(bezier, LIST); // ptlist = bezier_points(bezier, LIST);
// Topics: Bezier Curves
// Description: // Description:
// Computes points on a bezier curve with control points specified by `bezier` at parameter values // Computes points on a bezier curve with control points specified by `bezier` at parameter values
// specified by `u`, which can be a scalar or a list. The value `u=0` gives the first endpoint; `u=1` gives the final endpoint, // specified by `u`, which can be a scalar or a list. The value `u=0` gives the first endpoint; `u=1` gives the final endpoint,
@ -176,10 +178,11 @@ function _bezier_matrix(N) =
// Function: bezier_curve() // Function: bezier_curve()
// Synopsis: Computes a number of uniformly distributed points along a bezier curve.
// Topics: Bezier Curves
// See Also: bezier_curve(), bezier_curvature(), bezier_tangent(), bezier_derivative(), bezier_points()
// Usage: // Usage:
// path = bezier_curve(bezier, [splinesteps], [endpoint]); // path = bezier_curve(bezier, [splinesteps], [endpoint]);
// Topics: Bezier Curves
// See Also: bezier_curvature(), bezier_tangent(), bezier_derivative(), bezier_points()
// Description: // Description:
// Takes a list of bezier control points and generates splinesteps segments (splinesteps+1 points) // Takes a list of bezier control points and generates splinesteps segments (splinesteps+1 points)
// along the bezier curve they define. // along the bezier curve they define.
@ -210,12 +213,13 @@ function bezier_curve(bezier,splinesteps=16,endpoint=true) =
// Function: bezier_derivative() // Function: bezier_derivative()
// Synopsis: Evaluates the derivative of the bezier curve at the given point or points.
// Topics: Bezier Curves
// See Also: bezier_curvature(), bezier_tangent(), bezier_points()
// Usage: // Usage:
// deriv = bezier_derivative(bezier, u, [order]); // deriv = bezier_derivative(bezier, u, [order]);
// derivs = bezier_derivative(bezier, LIST, [order]); // derivs = bezier_derivative(bezier, LIST, [order]);
// derivs = bezier_derivative(bezier, RANGE, [order]); // derivs = bezier_derivative(bezier, RANGE, [order]);
// Topics: Bezier Curves
// See Also: bezier_curvature(), bezier_tangent(), bezier_points()
// Description: // Description:
// Evaluates the derivative of the bezier curve at the given parameter value or values, `u`. The `order` gives the order of the derivative. // Evaluates the derivative of the bezier curve at the given parameter value or values, `u`. The `order` gives the order of the derivative.
// The degree of the bezier curve is one less than the number of points in `bezier`. // The degree of the bezier curve is one less than the number of points in `bezier`.
@ -234,12 +238,13 @@ function bezier_derivative(bezier, u, order=1) =
// Function: bezier_tangent() // Function: bezier_tangent()
// Synopsis: Calculates unit tangent vectors along the bezier curve at one or more given positions.
// Topics: Bezier Curves
// See Also: bezier_curvature(), bezier_derivative(), bezier_points()
// Usage: // Usage:
// tanvec = bezier_tangent(bezier, u); // tanvec = bezier_tangent(bezier, u);
// tanvecs = bezier_tangent(bezier, LIST); // tanvecs = bezier_tangent(bezier, LIST);
// tanvecs = bezier_tangent(bezier, RANGE); // tanvecs = bezier_tangent(bezier, RANGE);
// Topics: Bezier Curves
// See Also: bezier_curvature(), bezier_derivative(), bezier_points()
// Description: // Description:
// Returns the unit tangent vector at the given parameter values on a bezier curve with control points `bezier`. // Returns the unit tangent vector at the given parameter values on a bezier curve with control points `bezier`.
// Arguments: // Arguments:
@ -254,12 +259,13 @@ function bezier_tangent(bezier, u) =
// Function: bezier_curvature() // Function: bezier_curvature()
// Synopsis: Returns the curvature values at one or more given positions along a bezier curve.
// Topics: Bezier Curves
// See Also: bezier_tangent(), bezier_derivative(), bezier_points()
// Usage: // Usage:
// crv = bezier_curvature(curve, u); // crv = bezier_curvature(curve, u);
// crvlist = bezier_curvature(curve, LIST); // crvlist = bezier_curvature(curve, LIST);
// crvlist = bezier_curvature(curve, RANGE); // crvlist = bezier_curvature(curve, RANGE);
// Topics: Bezier Curves
// See Also: bezier_tangent(), bezier_derivative(), bezier_points()
// Description: // Description:
// Returns the curvature value for the given parameters `u` on the bezier curve with control points `bezier`. // Returns the curvature value for the given parameters `u` on the bezier curve with control points `bezier`.
// The curvature is the inverse of the radius of the tangent circle at the given point. // The curvature is the inverse of the radius of the tangent circle at the given point.
@ -284,10 +290,11 @@ function bezier_curvature(bezier, u) =
// Function: bezier_closest_point() // Function: bezier_closest_point()
// Usage: // Synopsis: Finds the closest position on a bezier curve to a given point.
// u = bezier_closest_point(bezier, pt, [max_err]);
// Topics: Bezier Curves // Topics: Bezier Curves
// See Also: bezier_points() // See Also: bezier_points()
// Usage:
// u = bezier_closest_point(bezier, pt, [max_err]);
// Description: // Description:
// Finds the closest part of the given bezier curve to point `pt`. // Finds the closest part of the given bezier curve to point `pt`.
// The degree of the curve, N, is one less than the number of points in `curve`. // The degree of the curve, N, is one less than the number of points in `curve`.
@ -333,10 +340,11 @@ function bezier_closest_point(bezier, pt, max_err=0.01, u=0, end_u=1) =
// Function: bezier_length() // Function: bezier_length()
// Usage: // Synopsis: Approximate the length of part of a bezier curve.
// pathlen = bezier_length(bezier, [start_u], [end_u], [max_deflect]);
// Topics: Bezier Curves // Topics: Bezier Curves
// See Also: bezier_points() // See Also: bezier_points()
// Usage:
// pathlen = bezier_length(bezier, [start_u], [end_u], [max_deflect]);
// Description: // Description:
// Approximates the length of the portion of the bezier curve between start_u and end_u. // Approximates the length of the portion of the bezier curve between start_u and end_u.
// Arguments: // Arguments:
@ -370,10 +378,11 @@ function bezier_length(bezier, start_u=0, end_u=1, max_deflect=0.01) =
// Function: bezier_line_intersection() // Function: bezier_line_intersection()
// Usage: // Synopsis: Calculates where a bezier curve intersects a line.
// u = bezier_line_intersection(bezier, line);
// Topics: Bezier Curves, Geometry, Intersection // Topics: Bezier Curves, Geometry, Intersection
// See Also: bezier_points(), bezier_length(), bezier_closest_point() // See Also: bezier_points(), bezier_length(), bezier_closest_point()
// Usage:
// u = bezier_line_intersection(bezier, line);
// Description: // Description:
// Finds the intersection points of the 2D Bezier curve with control points `bezier` and the given line, specified as a pair of points. // Finds the intersection points of the 2D Bezier curve with control points `bezier` and the given line, specified as a pair of points.
// Returns the intersection as a list of `u` values for the Bezier. // Returns the intersection as a list of `u` values for the Bezier.
@ -404,12 +413,13 @@ function bezier_line_intersection(bezier, line) =
// Function: bezpath_points() // Function: bezpath_points()
// Synopsis: Computes one or more specified points along a bezier path.
// Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve()
// Usage: // Usage:
// pt = bezpath_points(bezpath, curveind, u, [N]); // pt = bezpath_points(bezpath, curveind, u, [N]);
// ptlist = bezpath_points(bezpath, curveind, LIST, [N]); // ptlist = bezpath_points(bezpath, curveind, LIST, [N]);
// path = bezpath_points(bezpath, curveind, RANGE, [N]); // path = bezpath_points(bezpath, curveind, RANGE, [N]);
// Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve()
// Description: // Description:
// Extracts from the Bezier path `bezpath` the control points for the Bezier curve whose index is `curveind` and // Extracts from the Bezier path `bezpath` the control points for the Bezier curve whose index is `curveind` and
// computes the point or points on the corresponding Bezier curve specified by `u`. If `curveind` is zero you // computes the point or points on the corresponding Bezier curve specified by `u`. If `curveind` is zero you
@ -424,12 +434,13 @@ function bezpath_points(bezpath, curveind, u, N=3) =
// Function: bezpath_curve() // Function: bezpath_curve()
// Synopsis: Takes a bezier path and converts it into a path of points.
// Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve(), bezpath_points()
// Usage: // Usage:
// path = bezpath_curve(bezpath, [splinesteps], [N], [endpoint]) // path = bezpath_curve(bezpath, [splinesteps], [N], [endpoint])
// Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve()
// Description: // Description:
// Takes a bezier path and converts it into a path of points. // Computes a number of uniformly distributed points along a bezier path.
// Arguments: // Arguments:
// bezpath = A bezier path to approximate. // bezpath = A bezier path to approximate.
// splinesteps = Number of straight lines to split each bezier curve into. default=16 // splinesteps = Number of straight lines to split each bezier curve into. default=16
@ -459,10 +470,11 @@ function bezpath_curve(bezpath, splinesteps=16, N=3, endpoint=true) =
// Function: bezpath_closest_point() // Function: bezpath_closest_point()
// Synopsis: Finds the closest part of a bezier path to a give point.
// Topics: Bezier Paths
// See Also: bezpath_points(), bezpath_curve(), bezier_points(), bezier_curve(), bezier_closest_point()
// Usage: // Usage:
// res = bezpath_closest_point(bezpath, pt, [N], [max_err]); // res = bezpath_closest_point(bezpath, pt, [N], [max_err]);
// Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve(), bezier_closest_point()
// Description: // Description:
// Finds an approximation to the closest part of the given bezier path to point `pt`. // Finds an approximation to the closest part of the given bezier path to point `pt`.
// Returns [segnum, u] for the closest position on the bezier path to the given point `pt`. // Returns [segnum, u] for the closest position on the bezier path to the given point `pt`.
@ -504,10 +516,11 @@ function bezpath_closest_point(bezpath, pt, N=3, max_err=0.01, seg=0, min_seg=un
// Function: bezpath_length() // Function: bezpath_length()
// Usage: // Synopsis: Approximate the length of a bezier path.
// plen = bezpath_length(path, [N], [max_deflect]);
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bezier_points(), bezier_curve(), bezier_length() // See Also: bezier_points(), bezier_curve(), bezier_length()
// Usage:
// plen = bezpath_length(path, [N], [max_deflect]);
// Description: // Description:
// Approximates the length of the bezier path. // Approximates the length of the bezier path.
// Arguments: // Arguments:
@ -530,10 +543,11 @@ function bezpath_length(bezpath, N=3, max_deflect=0.001) =
// Function: path_to_bezpath() // Function: path_to_bezpath()
// Usage: // Synopsis: Generates a bezier path that passes through all points in a given linear path.
// bezpath = path_to_bezpath(path, [closed], [tangents], [uniform], [size=]|[relsize=]);
// Topics: Bezier Paths, Rounding // Topics: Bezier Paths, Rounding
// See Also: path_tangents() // See Also: path_tangents()
// Usage:
// bezpath = path_to_bezpath(path, [closed], [tangents], [uniform], [size=]|[relsize=]);
// Description: // Description:
// Given a 2d or 3d input path and optional list of tangent vectors, computes a cubic (degree 3) bezier // Given a 2d or 3d input path and optional list of tangent vectors, computes a cubic (degree 3) bezier
// path that passes through every point on the input path and matches the tangent vectors. If you do // path that passes through every point on the input path and matches the tangent vectors. If you do
@ -616,10 +630,11 @@ function path_to_bezpath(path, closed, tangents, uniform=false, size, relsize) =
// Function: bezpath_close_to_axis() // Function: bezpath_close_to_axis()
// Usage: // Synopsis: Closes a 2D bezier path to the specified axis.
// bezpath = bezpath_close_to_axis(bezpath, [axis], [N]);
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bezpath_offset() // See Also: bezpath_offset()
// Usage:
// bezpath = bezpath_close_to_axis(bezpath, [axis], [N]);
// Description: // Description:
// Takes a 2D bezier path and closes it to the specified axis. // Takes a 2D bezier path and closes it to the specified axis.
// Arguments: // Arguments:
@ -659,10 +674,11 @@ function bezpath_close_to_axis(bezpath, axis="X", N=3) =
// Function: bezpath_offset() // Function: bezpath_offset()
// Usage: // Synopsis: Forms a closed bezier path loop with a translated and reversed copy of itself.
// bezpath = bezpath_offset(offset, bezier, [N]);
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bezpath_close_to_axis() // See Also: bezpath_close_to_axis()
// Usage:
// bezpath = bezpath_offset(offset, bezier, [N]);
// Description: // Description:
// Takes a 2D bezier path and closes it with a matching reversed path that is offset by the given `offset` [X,Y] distance. // Takes a 2D bezier path and closes it with a matching reversed path that is offset by the given `offset` [X,Y] distance.
// Arguments: // Arguments:
@ -697,6 +713,7 @@ function bezpath_offset(offset, bezier, N=3) =
// Section: Cubic Bezier Path Construction // Section: Cubic Bezier Path Construction
// Function: bez_begin() // Function: bez_begin()
// Synopsis: Calculates starting bezier path control points.
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bez_tang(), bez_joint(), bez_end() // See Also: bez_tang(), bez_joint(), bez_end()
// Usage: // Usage:
@ -767,6 +784,7 @@ function bez_begin(pt,a,r,p) =
// Function: bez_tang() // Function: bez_tang()
// Synopsis: Calculates control points for a smooth bezier path joint.
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bez_begin(), bez_joint(), bez_end() // See Also: bez_begin(), bez_joint(), bez_end()
// Usage: // Usage:
@ -802,6 +820,7 @@ function bez_tang(pt,a,r1,r2,p) =
// Function: bez_joint() // Function: bez_joint()
// Synopsis: Calculates control points for a disjointed corner bezier path joint.
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bez_begin(), bez_tang(), bez_end() // See Also: bez_begin(), bez_tang(), bez_end()
// Usage: // Usage:
@ -842,6 +861,7 @@ function bez_joint(pt,a1,a2,r1,r2,p1,p2) =
// Function: bez_end() // Function: bez_end()
// Synopsis: Calculates ending bezier path control points.
// Topics: Bezier Paths // Topics: Bezier Paths
// See Also: bez_tang(), bez_joint(), bez_end() // See Also: bez_tang(), bez_joint(), bez_end()
// Usage: // Usage:
@ -868,11 +888,12 @@ function bez_end(pt,a,r,p) =
// Function: is_bezier_patch() // Function: is_bezier_patch()
// Synopsis: Returns true if the given item is a bezier patch.
// Topics: Bezier Patches, Type Checking
// Usage: // Usage:
// bool = is_bezier_patch(x); // bool = is_bezier_patch(x);
// Topics: Bezier Patches, Type Checking
// Description: // Description:
// Returns true if the given item is a bezier patch. // Returns true if the given item is a bezier patch. (a 2D array of 3D points.)
// Arguments: // Arguments:
// x = The value to check the type of. // x = The value to check the type of.
function is_bezier_patch(x) = function is_bezier_patch(x) =
@ -880,10 +901,11 @@ function is_bezier_patch(x) =
// Function: bezier_patch_flat() // Function: bezier_patch_flat()
// Usage: // Synopsis: Creates a flat bezier patch.
// patch = bezier_patch_flat(size, [N=], [spin=], [orient=], [trans=]);
// Topics: Bezier Patches // Topics: Bezier Patches
// See Also: bezier_patch_points() // See Also: bezier_patch_points()
// Usage:
// patch = bezier_patch_flat(size, [N=], [spin=], [orient=], [trans=]);
// Description: // Description:
// Returns a flat rectangular bezier patch of degree `N`, centered on the XY plane. // Returns a flat rectangular bezier patch of degree `N`, centered on the XY plane.
// Arguments: // Arguments:
@ -913,10 +935,11 @@ function bezier_patch_flat(size, N=1, spin=0, orient=UP, trans=[0,0,0]) =
// Function: bezier_patch_reverse() // Function: bezier_patch_reverse()
// Usage: // Synopsis: Reverses the orientation of a bezier patch.
// rpatch = bezier_patch_reverse(patch);
// Topics: Bezier Patches // Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_patch_flat() // See Also: bezier_patch_points(), bezier_patch_flat()
// Usage:
// rpatch = bezier_patch_reverse(patch);
// Description: // Description:
// Reverses the patch, so that the faces generated from it are flipped back to front. // Reverses the patch, so that the faces generated from it are flipped back to front.
// Arguments: // Arguments:
@ -926,12 +949,13 @@ function bezier_patch_reverse(patch) =
// Function: bezier_patch_points() // Function: bezier_patch_points()
// Synopsis: Computes one or more specified points across a bezier surface patch.
// Topics: Bezier Patches
// See Also: bezier_patch_normals(), bezier_points(), bezier_curve(), bezpath_curve()
// Usage: // Usage:
// pt = bezier_patch_points(patch, u, v); // pt = bezier_patch_points(patch, u, v);
// ptgrid = bezier_patch_points(patch, LIST, LIST); // ptgrid = bezier_patch_points(patch, LIST, LIST);
// ptgrid = bezier_patch_points(patch, RANGE, RANGE); // ptgrid = bezier_patch_points(patch, RANGE, RANGE);
// Topics: Bezier Patches
// See Also: bezier_patch_normals(), bezier_points(), bezier_curve(), bezpath_curve()
// Description: // Description:
// Sample a bezier patch on a listed point set. The bezier patch must be a rectangular array of // 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 // points, and it will be sampled at all the (u,v) pairs that you specify. If you give u and v
@ -987,10 +1011,11 @@ function _bezier_rectangle(patch, splinesteps=16, style="default") =
// Function: bezier_vnf() // Function: bezier_vnf()
// Usage: // Synopsis: Generates a (probably non-manifold) VNF for one or more bezier surface patches.
// vnf = bezier_vnf(patches, [splinesteps], [style]);
// Topics: Bezier Patches // Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_patch_flat() // See Also: bezier_patch_points(), bezier_patch_flat()
// Usage:
// vnf = bezier_vnf(patches, [splinesteps], [style]);
// Description: // Description:
// Convert a patch or list of patches into the corresponding Bezier surface, representing the // Convert a patch or list of patches into the corresponding Bezier surface, representing the
// result as a [VNF structure](vnf.scad). The `splinesteps` argument specifies the sampling grid of // result as a [VNF structure](vnf.scad). The `splinesteps` argument specifies the sampling grid of
@ -1113,6 +1138,9 @@ function bezier_vnf(patches=[], splinesteps=16, style="default") =
// Function: bezier_vnf_degenerate_patch() // Function: bezier_vnf_degenerate_patch()
// Synopsis: Generates a VNF for a degenerate bezier surface patch.
// Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_patch_flat(), bezier_vnf()
// Usage: // Usage:
// vnf = bezier_vnf_degenerate_patch(patch, [splinesteps], [reverse]); // vnf = bezier_vnf_degenerate_patch(patch, [splinesteps], [reverse]);
// vnf_edges = bezier_vnf_degenerate_patch(patch, [splinesteps], [reverse], return_edges=true); // vnf_edges = bezier_vnf_degenerate_patch(patch, [splinesteps], [reverse], return_edges=true);
@ -1297,12 +1325,13 @@ function bezier_vnf_degenerate_patch(patch, splinesteps=16, reverse=false, retur
// Function: bezier_patch_normals() // Function: bezier_patch_normals()
// Synopsis: Computes surface normals for one or more places on a bezier surface patch.
// Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_points(), bezier_curve(), bezpath_curve()
// Usage: // Usage:
// n = bezier_patch_normals(patch, u, v); // n = bezier_patch_normals(patch, u, v);
// ngrid = bezier_patch_normals(patch, LIST, LIST); // ngrid = bezier_patch_normals(patch, LIST, LIST);
// ngrid = bezier_patch_normals(patch, RANGE, RANGE); // ngrid = bezier_patch_normals(patch, RANGE, RANGE);
// Topics: Bezier Patches
// See Also: bezier_patch_points(), bezier_points(), bezier_curve(), bezpath_curve()
// Description: // Description:
// Compute the unit normal vector to a bezier patch at the listed point set. The bezier patch must be a rectangular array of // Compute the unit 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 // points, and the normal will be computed at all the (u,v) pairs that you specify. If you give u and v
@ -1409,10 +1438,11 @@ function bezier_patch_normals(patch, u, v) =
// Module: debug_bezier() // Module: debug_bezier()
// Usage: // Synopsis: Shows a bezier path and it's associated control points.
// debug_bezier(bez, [size], [N=]);
// Topics: Bezier Paths, Debugging // Topics: Bezier Paths, Debugging
// See Also: bezpath_curve() // See Also: bezpath_curve()
// Usage:
// debug_bezier(bez, [size], [N=]);
// Description: // Description:
// Renders 2D or 3D bezier paths and their associated control points. // Renders 2D or 3D bezier paths and their associated control points.
// Useful for debugging bezier paths. // Useful for debugging bezier paths.
@ -1462,10 +1492,11 @@ module debug_bezier(bezpath, width=1, N=3) {
// Module: debug_bezier_patches() // Module: debug_bezier_patches()
// Usage: // Synopsis: Shows a bezier surface patch and its associated control points.
// debug_bezier_patches(patches, [size=], [splinesteps=], [showcps=], [showdots=], [showpatch=], [convexity=], [style=]);
// Topics: Bezier Patches, Debugging // Topics: Bezier Patches, Debugging
// See Also: bezier_patch_points(), bezier_patch_flat(), bezier_vnf() // See Also: bezier_patch_points(), bezier_patch_flat(), bezier_vnf()
// Usage:
// debug_bezier_patches(patches, [size=], [splinesteps=], [showcps=], [showdots=], [showpatch=], [convexity=], [style=]);
// Description: // Description:
// Shows the surface, and optionally, control points of a list of bezier patches. // Shows the surface, and optionally, control points of a list of bezier patches.
// Arguments: // Arguments: