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include beziers.scad in std.scad, remove include line from all other files containing it

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Alex Matulich 2025-01-05 11:40:20 -08:00
parent 5e96d1772e
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4
WRITING_DOCS.md
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@ -135,7 +135,7 @@ To declare what code the user needs to add to their code to include or use this
// Includes: // Includes:
// include <BOSL2/std.scad> // include <BOSL2/std.scad>
// include <BOSL2/beziers.scad> // include <BOSL2/gears.scad>
Which outputs Markdown code that renders like: Which outputs Markdown code that renders like:
@ -145,7 +145,7 @@ Which outputs Markdown code that renders like:
> >
> ```openscad > ```openscad
> include <BOSL2/std.scad> > include <BOSL2/std.scad>
> include <BOSL2/beziers.scad> > include <BOSL2/gears.scad>
> ``` > ```

2
beziers.scad
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@ -8,9 +8,9 @@
// computing the Bezier curves and surfaces given by the control points, // computing the Bezier curves and surfaces given by the control points,
// Includes: // Includes:
// include <BOSL2/std.scad> // include <BOSL2/std.scad>
// include <BOSL2/beziers.scad>
// FileGroup: Advanced Modeling // FileGroup: Advanced Modeling
// FileSummary: Bezier curves and surfaces. // FileSummary: Bezier curves and surfaces.
// FileFootnotes: STD=Included in std.scad
////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////
// Terminology: // Terminology:

1
examples/BOSL2logo.scad
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@ -1,6 +1,5 @@
include <BOSL2/std.scad> include <BOSL2/std.scad>
include <BOSL2/gears.scad> include <BOSL2/gears.scad>
include <BOSL2/beziers.scad>
include <BOSL2/screws.scad> include <BOSL2/screws.scad>
include <BOSL2/cubetruss.scad> include <BOSL2/cubetruss.scad>

1
examples/spherical_patch.scad
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@ -1,5 +1,4 @@
include <BOSL2/std.scad> include <BOSL2/std.scad>
include <BOSL2/beziers.scad>
// Makes a pseudo-sphere from a rectangular patch and its mirror. // Makes a pseudo-sphere from a rectangular patch and its mirror.
s = 50/sqrt(2); s = 50/sqrt(2);

1
miscellaneous.scad
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@ -90,7 +90,6 @@ module extrude_from_to(pt1, pt2, convexity, twist, scale, slices) {
// path_extrude2d(arc(d=100,angle=[180,270]),caps=true) // path_extrude2d(arc(d=100,angle=[180,270]),caps=true)
// trapezoid(w1=10, w2=5, h=10, anchor=BACK); // trapezoid(w1=10, w2=5, h=10, anchor=BACK);
// Example: // Example:
// include <BOSL2/beziers.scad>
// path = bezpath_curve([ // path = bezpath_curve([
// [-50,0], [-25,50], [0,0], [50,0] // [-50,0], [-25,50], [0,0], [50,0]
// ]); // ]);

1
nurbs.scad
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@ -15,7 +15,6 @@
////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
// Section: NURBS Curves // Section: NURBS Curves

1
rounding.scad
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@ -11,7 +11,6 @@
// FileGroup: Advanced Modeling // FileGroup: Advanced Modeling
// FileSummary: Round path corners, rounded prisms, rounded cutouts in tubes, filleted prism joints // FileSummary: Round path corners, rounded prisms, rounded cutouts in tubes, filleted prism joints
////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////
include <beziers.scad>
include <structs.scad> include <structs.scad>
// Section: Types of Roundovers // Section: Types of Roundovers

1
shapes2d.scad
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@ -16,7 +16,6 @@
////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////
use <builtins.scad> use <builtins.scad>
include <beziers.scad>

1
skin.scad
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@ -934,7 +934,6 @@ function linear_sweep(
// texture=tex, tex_size=[20,20], // texture=tex, tex_size=[20,20],
// tex_depth=1, style="concave"); // tex_depth=1, style="concave");
// Example: // Example:
// include <BOSL2/beziers.scad>
// bezpath = [ // bezpath = [
// [15, 30], [10,15], // [15, 30], [10,15],
// [10, 0], [20, 10], [30,12], // [10, 0], [20, 10], [30,12],

1
std.scad
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@ -16,6 +16,7 @@ include <distributors.scad>
include <miscellaneous.scad> include <miscellaneous.scad>
include <color.scad> include <color.scad>
include <attachments.scad> include <attachments.scad>
include <beziers.scad>
include <shapes3d.scad> include <shapes3d.scad>
include <shapes2d.scad> include <shapes2d.scad>
include <drawing.scad> include <drawing.scad>

44
tutorials/Beziers_for_Beginners.md
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@ -9,12 +9,10 @@ Quadratic Béziers, i.e. Bezier's of degree 2, are defined by [quadratic polynom
![Image courtesy Wikipedia](images/bezier_2_big.gif "Quadratic Bézier Animation courtesy Wikipedia") ![Image courtesy Wikipedia](images/bezier_2_big.gif "Quadratic Bézier Animation courtesy Wikipedia")
To visualize a Bézier curve we can use the module [debug_bezier()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#module-debug_bezier). The argument N tells debug_bezier the degree of the Bézier curve. To visualize a Bézier curve we can use the module [debug_bezier()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#module-debug_bezier). The argument N tells debug_bezier the degree of the Bézier curve.
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[0,0], [30,60], [0,100]]; bez = [[0,0], [30,60], [0,100]];
debug_bezier(bez, N = 2); debug_bezier(bez, N = 2);
@ -24,7 +22,6 @@ If we move any of the control points, we change the shape of the curve.
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[0,0], [100,50], [0,100]]; bez = [[0,0], [100,50], [0,100]];
debug_bezier(bez, N = 2); debug_bezier(bez, N = 2);
@ -36,7 +33,6 @@ Cubic Bézier curves (degree 3) are defined by cubic polynomials. A cubic Bézie
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [100,40], [50,90], [25,80]]; bez = [[20,0], [100,40], [50,90], [25,80]];
debug_bezier(bez, N = 3); debug_bezier(bez, N = 3);
@ -46,7 +42,6 @@ By moving the second and third points on the list we change the shape of the cur
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
debug_bezier(bez, N = 3); debug_bezier(bez, N = 3);
@ -63,7 +58,6 @@ Higher order Béziers such as Quartic (degree 4) and Quintic (degree 5) Béziers
```openscad-2D;Anim;FrameMS=2000;Frames=4;VPT=[50,50,40];ImgOnly ```openscad-2D;Anim;FrameMS=2000;Frames=4;VPT=[50,50,40];ImgOnly
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [ bez = [
[[0,0], [100,100], [0,80]], [[0,0], [100,100], [0,80]],
@ -80,7 +74,6 @@ Bézier curves are not restricted to the XY plane. We can define a 3d Bézier a
```openscad-2D;FlatSpin,VPR=[80,0,360*$t],VPT=[0,0,20],VPD=175 ```openscad-2D;FlatSpin,VPR=[80,0,360*$t],VPT=[0,0,20],VPD=175
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[10,0,10], [30,30,-10], [-30,30,40], [-10,0,30]]; bez = [[10,0,10], [30,30,-10], [-30,30,40], [-10,0,30]];
debug_bezier(bez, N = 3); debug_bezier(bez, N = 3);
@ -100,7 +93,6 @@ The list of control points for a Bézier is not an OpenSCAD path. If we treat th
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[0,0], [30,30], [0,50], {70,30] [0,100]]; bez = [[0,0], [30,30], [0,50], {70,30] [0,100]];
debug_bezier(bez, N = 2); debug_bezier(bez, N = 2);
@ -110,7 +102,6 @@ While the bez variable in these examples is a list of points, it is not the same
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
debug_bezier(bez, N = 3); debug_bezier(bez, N = 3);
@ -121,7 +112,6 @@ color("red") stroke(bez);
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
path = bezpath_curve(bez, N = 3); path = bezpath_curve(bez, N = 3);
@ -134,7 +124,6 @@ This means that a series of 7 control points can be grouped into three (overlapp
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[0,0], [10,30], [20,0], [30,-30], [40,0], [50,30],[60,0]]; bez = [[0,0], [10,30], [20,0], [30,-30], [40,0], [50,30],[60,0]];
path = bezpath_curve(bez, N = 2); //make a quadratic Bézier path path = bezpath_curve(bez, N = 2); //make a quadratic Bézier path
@ -143,7 +132,6 @@ stroke(path);
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[0,0], [10,30], [20,0], [30,-30], [40,0], [50,30],[60,0]]; bez = [[0,0], [10,30], [20,0], [30,-30], [40,0], [50,30],[60,0]];
path = bezpath_curve(bez, N=3); //make a cubic Bézier path path = bezpath_curve(bez, N=3); //make a cubic Bézier path
@ -154,7 +142,6 @@ By default [bezpath_curve()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.sc
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
path = bezpath_curve(bez, splinesteps = 6); path = bezpath_curve(bez, splinesteps = 6);
@ -165,7 +152,6 @@ To close the path to the y-axis we can use the [bezpath\_close\_to\_axis()](http
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
closed = bezpath_close_to_axis(bez, axis = "Y"); closed = bezpath_close_to_axis(bez, axis = "Y");
@ -177,7 +163,6 @@ If we use [rotate_sweep()](https://github.com/BelfrySCAD/BOSL2/wiki/skin.scad#fu
```openscad-3D VPR = [80,0,20] ```openscad-3D VPR = [80,0,20]
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
$fn = 72; $fn = 72;
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
@ -190,7 +175,6 @@ Instead of closing the path all the way to the y-axis, we can use [bezpath_offse
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
$fn = 72; $fn = 72;
bez = [[20,0], [60,40], [-20,50], [25,80]]; bez = [[20,0], [60,40], [-20,50], [25,80]];
@ -207,7 +191,6 @@ You can see the differences between the three methods here, with [bezpath_offset
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
include<BOSL2/rounding.scad> include<BOSL2/rounding.scad>
$fn = 72; $fn = 72;
@ -230,7 +213,6 @@ Sweeping a Bézier path offset using any of the three methods around the y-axis
```openscad-3D, VPT=[0,60,40], VPR=[90,0,0], VPD=250 ```openscad-3D, VPT=[0,60,40], VPR=[90,0,0], VPD=250
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
include<BOSL2/rounding.scad> include<BOSL2/rounding.scad>
$fn = 72; $fn = 72;
@ -240,16 +222,14 @@ path = offset_stroke(bezier_curve(bez, splinesteps = 32), [2,0]);
back_half(s = 200) rotate_sweep(path,360); back_half(s = 200) rotate_sweep(path,360);
``` ```
We'll use a cylinder with a height of 2 for the floor of our vase. At the bottom of the vase the radius of the hole is bez[0].x but we need to find the radius at y = 2. The function [bezier_line_intersection()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bezier_line_intersection) will return a list of u-values where a given line intersects our Bézier curve. We'll use a cylinder with a height of 2 for the floor of our vase. At the bottom of the vase the radius of the hole is bez[0].x but we need to find the radius at y = 2. The function [bezier_line_intersection()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bezier_line_intersection) returns a list of u-values where a given line intersects our Bézier curve.
The u-value is a number between 0 and 1 that designates how far along the curve the intersections occur. In our case the line only crosses the Bézier at one point so we get the single-element list [0.0168783]. The u-value is a number between 0 and 1 that designates how far along the curve the intersections occur. In our case the line only crosses the Bézier at one point so we get the single-element list [0.0168783].
The function [bezier_points()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bezpath_points) will convert that list of u-values to a list of x,y coordinates. Drawing a line at y = 2 gives us the single-element list [[17.1687, 2]]. The function [bezier_points()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bezpath_points) converts that list of u-values to a list of x,y coordinates. Drawing a line at y = 2 gives us the single-element list [[17.1687, 2]].
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = [[15,0], [60,40], [-25,50], [25,80]]; bez = [[15,0], [60,40], [-25,50], [25,80]];
debug_bezier(bez, N = 3); debug_bezier(bez, N = 3);
@ -260,11 +240,10 @@ echo(bezier_points(bez,u)); // [[17.1687, 2]]
``` ```
That means a cyl() with a height of 2, a bottom radius of bez[0].x and a top radius of 17.1687 will fit our vase. That means a cyl() with a height of 2, a bottom radius of bez[0].x and a top radius of 17.1687 fits our vase.
```openscad-3D, VPT=[0,60,12], VPR=[90,0,0], VPD=150 ```openscad-3D, VPT=[0,60,12], VPR=[90,0,0], VPD=150
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
include<BOSL2/rounding.scad> include<BOSL2/rounding.scad>
$fn = 72; $fn = 72;
@ -282,7 +261,6 @@ Keep in mind the fact that **$fn** controls the smoothness of the [rotate_sweep(
```openscad-3D NoAxes VPD=400 VPT=[45,45,10] Big ```openscad-3D NoAxes VPD=400 VPT=[45,45,10] Big
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
$fn = 72; $fn = 72;
@ -311,7 +289,6 @@ First, you can specify the endpoints by vectors and the control points by angle,
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], 45, 42.43), bez_begin([0,0], 45, 42.43),
bez_end([100,0], 90, 30), bez_end([100,0], 90, 30),
@ -323,7 +300,6 @@ Second, can specify the XY location of the endpoint and that end's control point
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], [30,30]), bez_begin([0,0], [30,30]),
bez_end([100,0], [0,30]), bez_end([100,0], [0,30]),
@ -335,7 +311,6 @@ Third, you can specify the endpoints by vectors, and the control points by a dir
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], BACK+RIGHT, 42.43), bez_begin([0,0], BACK+RIGHT, 42.43),
bez_end([100,0], [0,1], 30), bez_end([100,0], [0,1], 30),
@ -349,7 +324,6 @@ Here's an example using angle and distance to specify a corner. Note that the an
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], 45, 42.43), bez_begin([0,0], 45, 42.43),
bez_joint([40,20], 90,0, 30,30), bez_joint([40,20], 90,0, 30,30),
@ -358,13 +332,12 @@ bez = flatten([
debug_bezier(bez,N=3); debug_bezier(bez,N=3);
``` ```
The fourth cubic Bézier path constructor is [bez_tang()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bez_tang). This constructor makes smooth joint. It also has three control points, one on the path and the approaching and departing control points. Because all three points lie on a single line, we need only specify the angle of the departing control point. As in this example you can specify different distances for the approaching and departing controls points. If you specify only a single distance, it will be used for both. The fourth cubic Bézier path constructor is [bez_tang()](https://github.com/BelfrySCAD/BOSL2/wiki/beziers.scad#function-bez_tang). This constructor makes smooth joint. It also has three control points, one on the path and the approaching and departing control points. Because all three points lie on a single line, we need only specify the angle of the departing control point. As in this example you can specify different distances for the approaching and departing controls points. If you specify only a single distance, it is used for both.
We can add a smooth joint to the last example: We can add a smooth joint to the last example:
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], 45, 42.43), bez_begin([0,0], 45, 42.43),
bez_joint([40,20], 90,0, 30,30), bez_joint([40,20], 90,0, 30,30),
@ -378,7 +351,6 @@ It is not necessary to use the same notation to describe the entire Bézier path
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], [30,30]), bez_begin([0,0], [30,30]),
bez_joint([40,20], BACK,RIGHT, 30,30), bez_joint([40,20], BACK,RIGHT, 30,30),
@ -403,7 +375,6 @@ where r is the radius of the circle and n is the number of bez_tang() segments r
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
r = 50; // radius of the circle r = 50; // radius of the circle
n = 4; //bezier segments to complete circle n = 4; //bezier segments to complete circle
@ -424,7 +395,6 @@ Similarly, for the heart-shaped path we'll replace a corner point with the start
```openscad-2D ```openscad-2D
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,25], 40, 40), bez_begin([0,25], 40, 40),
@ -438,7 +408,6 @@ The first shape in [The Bézier Game](https://bezier.method.ac) past the stages
```openscad-3D,Big,NoScales,VPR=[0,0,0],VPT=[100,25,0],VPF=22 ```openscad-3D,Big,NoScales,VPR=[0,0,0],VPT=[100,25,0],VPF=22
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([0,0], BACK, 15), bez_begin([0,0], BACK, 15),
@ -468,7 +437,6 @@ We can make a heart shaped dish using a 2D Bézier path to define the shape. Wh
```openscad-3d ```openscad-3d
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
include<BOSL2/rounding.scad> include<BOSL2/rounding.scad>
bez = flatten([ bez = flatten([
@ -494,7 +462,6 @@ The path by angle constructors can be used to create 3D Bézier paths by specify
```openscad-3D,FlatSpin,NoScales,VPR=[85,0,360*$t],VPT=[0,0,20] ```openscad-3D,FlatSpin,NoScales,VPR=[85,0,360*$t],VPT=[0,0,20]
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin ([-50,0,0], 90, 25, p=90), bez_begin ([-50,0,0], 90, 25, p=90),
@ -512,7 +479,6 @@ The cubic Bézier path constructors can also be used to create 3D Bézier paths
```openscad-3D,FlatSpin,NoScales,VPR=[80,0,360*$t],,VPT=[0,0,20] ```openscad-3D,FlatSpin,NoScales,VPR=[80,0,360*$t],,VPT=[0,0,20]
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([-50,0,0], [0,25,0]), bez_begin([-50,0,0], [0,25,0]),
@ -531,7 +497,6 @@ The third method for specifying 3D cubic Bézier Paths is by Direction Vector an
```openscad-3D,FlatSpin,NoScales,VPR=[80,0,360*$t],,VPT=[0,0,20] ```openscad-3D,FlatSpin,NoScales,VPR=[80,0,360*$t],,VPT=[0,0,20]
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
bez = flatten([ bez = flatten([
bez_begin([-50,0,0], BACK, 25), bez_begin([-50,0,0], BACK, 25),
@ -550,7 +515,6 @@ We can use a 2D Bézier path to define the shape of our bud vase as we did in th
```openscad-3d,Big ```openscad-3d,Big
include<BOSL2/std.scad> include<BOSL2/std.scad>
include<BOSL2/beziers.scad>
//Side Bézier Path //Side Bézier Path
side_bez = [[20,0], [40,40], [-10,70], [20,100]]; side_bez = [[20,0], [40,40], [-10,70], [20,100]];

4
vnf.scad
View file

@ -322,7 +322,6 @@ function vnf_vertex_array(
// vnf_wireframe(vnf,width=0.1); // vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9); // color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
// Example(3D,NoAxes,Edges,VPR=[65,0,25],VPD=380,Med): Model of a cymbal with roughly same-size facets, using a different number of points for each concentric ring of vertices. // Example(3D,NoAxes,Edges,VPR=[65,0,25],VPD=380,Med): Model of a cymbal with roughly same-size facets, using a different number of points for each concentric ring of vertices.
// include <BOSL2/beziers.scad>
// bez = [ // bez = [
// [[0,26], [35,26], [29,0], [80,16], [102,0]], //top // [[0,26], [35,26], [29,0], [80,16], [102,0]], //top
// [[99,-1], [79,15], [28,-1], [34,25], [-1,25]] // bottom // [[99,-1], [79,15], [28,-1], [34,25], [-1,25]] // bottom
@ -1443,7 +1442,6 @@ function projection(vnf,cut=false,eps=EPSILON) =
// vnf4=vnf_join([vnf3, zflip(vnf3,1)]); // vnf4=vnf_join([vnf3, zflip(vnf3,1)]);
// vnf_polyhedron(vnf4); // vnf_polyhedron(vnf4);
// Example: When the input VNF is a surface with a boundary, if you use the default setting closed=true, then vnf_halfspace() tries to construct closing faces from the edges created by the cut. These faces may be invalid, for example if the cut points are collinear. In this example the constructed face is a valid face. // Example: When the input VNF is a surface with a boundary, if you use the default setting closed=true, then vnf_halfspace() tries to construct closing faces from the edges created by the cut. These faces may be invalid, for example if the cut points are collinear. In this example the constructed face is a valid face.
// include <BOSL2/beziers.scad>
// patch=[ // patch=[
// [[10,-10,0],[1,-1,0],[-1,-1,0],[-10,-10,0]], // [[10,-10,0],[1,-1,0],[-1,-1,0],[-10,-10,0]],
// [[10,-10,20],[1,-1,20],[-1,-1,20],[-10,-10,20]] // [[10,-10,20],[1,-1,20],[-1,-1,20],[-10,-10,20]]
@ -1452,7 +1450,6 @@ function projection(vnf,cut=false,eps=EPSILON) =
// vnfcut = vnf_halfspace([-.8,0,-1,-14],vnf); // vnfcut = vnf_halfspace([-.8,0,-1,-14],vnf);
// vnf_polyhedron(vnfcut); // vnf_polyhedron(vnfcut);
// Example: Setting closed to false eliminates this (possibly invalid) face: // Example: Setting closed to false eliminates this (possibly invalid) face:
// include <BOSL2/beziers.scad>
// patch=[ // patch=[
// [[10,-10,0],[1,-1,0],[-1,-1,0],[-10,-10,0]], // [[10,-10,0],[1,-1,0],[-1,-1,0],[-10,-10,0]],
// [[10,-10,20],[1,-1,20],[-1,-1,20],[-10,-10,20]] // [[10,-10,20],[1,-1,20],[-1,-1,20],[-10,-10,20]]
@ -1775,7 +1772,6 @@ function _sort_pairs0(arr) =
// merge = set to false to suppress the automatic invocation of {{vnf_merge_points()}}. Default: true // merge = set to false to suppress the automatic invocation of {{vnf_merge_points()}}. Default: true
// idx = if true, return indices into VNF vertices instead of actual 3D points. Must set `merge=false` to enable this. Default: false // idx = if true, return indices into VNF vertices instead of actual 3D points. Must set `merge=false` to enable this. Default: false
// Example(3D,NoAxes,VPT=[7.06325,-20.8414,20.1803],VPD=292.705,VPR=[55,0,25.7]): In this example we know that the bezier patch VNF has no duplicate vertices, so we do not need to run {{vnf_merge_points()}}. // Example(3D,NoAxes,VPT=[7.06325,-20.8414,20.1803],VPD=292.705,VPR=[55,0,25.7]): In this example we know that the bezier patch VNF has no duplicate vertices, so we do not need to run {{vnf_merge_points()}}.
// include <BOSL2/beziers.scad>
// patch = [ // patch = [
// // u=0,v=0 u=1,v=0 // // u=0,v=0 u=1,v=0
// [[-50,-50, 0], [-16,-50, 20], [ 16,-50, -20], [50,-50, 0]], // [[-50,-50, 0], [-16,-50, 20], [ 16,-50, -20], [50,-50, 0]],