User:LABoyd2/polyhedron to manual 160313

polyhedron
A polyhedron is the most general 3D primitive solid. It can be used to create any regular or irregular shape including those with concave as well as convex features. Curved surfaces are approximated by a series of flat surfaces.

polyhedron( points = [ [X0, Y0, Z0], [X1, Y1, Z1], ... ], triangles = [ [P0, P1, P2], ... ], convexity = N);  // before 2014.03 polyhedron( points = [ [X0, Y0, Z0], [X1, Y1, Z1], ... ], faces = [ [P0, P1, P2, P3, ...], ... ], convexity = N);  // 2014.03 & later


 * Parameters
 * points
 * Vector of 3d points or vertices. Each point is in turn a vector, [x,y,z], of its coordinates.
 * Points may be defined in any order. N points are referenced, in the order defined, as 0 to N-1.


 * triangles       (deprecated in version 2014.03, use faces)
 * Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 points from the points vector.


 * faces           (introduced in version 2014.03)
 * Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 or more points from the points vector.
 * Faces may be defined in any order. Define enough faces to fully enclose the solid, with no overlap.
 * Points which describe a single face must all be on the same plane.


 * convexity
 * Integer. The convexity parameter specifies the maximum number of faces a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode. It has no effect on the polyhedron rendering. For display problems, setting it to 10 should work fine for most cases.

default values: polyhedron; yields: polyhedron(points = undef, faces = undef, convexity = 1);

All faces must have points ordered in the same direction. OpenSCAD prefers clockwise when looking at each face from outside inwards. The back is viewed from the back, the bottom from the bottom, etc..


 * Example 1 Using polyhedron to generate cube( [ 10, 7, 5 ] );

CubePoints = [ [ 0,  0,  0 ],  //0   [ 10,  0,  0 ],  //1   [ 10,  7,  0 ],  //2   [  0,  7,  0 ],  //3   [  0,  0,  5 ],  //4   [ 10,  0,  5 ],  //5   [ 10,  7,  5 ],  //6   [  0,  7,  5 ]]; //7 CubeFaces = [ [0,1,2,3], // bottom [4,5,1,0], // front [7,6,5,4], // top [5,6,2,1], // right [6,7,3,2], // back [7,4,0,3]]; // left polyhedron( CubePoints, CubeFaces );

equivalent descriptions of the bottom face [0,1,2,3],  [0,1,2,3,0],   [1,2,3,0],   [2,3,0,1],   [3,0,1,2],   [0,1,2],[2,3,0],   // 2 triangles with no overlap [1,2,3],[3,0,1],  [1,2,3],[0,1,3],
 * Example 2 A square base pyramid:

polyhedron(  points=[ [10,10,0],[10,-10,0],[-10,-10,0],[-10,10,0], // the four points at base            [0,0,10]  ],                                 // the apex point    faces=[ [0,1,4],[1,2,4],[2,3,4],[3,0,4],              // each triangle side               [1,0,3],[2,1,3] ]                         // two triangles for square base  );

Debugging polyhedrons
Mistakes in defining polyhedrons include not having all faces with the same order, overlap of faces and missing faces or portions of faces.

When viewed from the outside, the points describing each face must be in the same order. OpenSCAD prefers CW, and provides a mechanism for detecting CCW. When the thrown together view (F12) is used with F5, CCW faces are shown in pink. Reorder the points for incorrect faces. Rotate the object to view all faces. The pink view can be turned off with F10.

OpenSCAD allows, temporarily, commenting out part of the face descriptions so that only the remaining faces are displayed. Use // to comment out the rest of the line. Use /* and */ to start and end a comment block. This can be part of a line or extend over several lines. Viewing only part of the faces can be helpful in determining the right points for an individual face. Note that a solid is not shown, only the faces. If using F12, all faces have one pink side.



CubeFaces = [ /* [0,1,2,3], // bottom [4,5,1,0], // front */ [7,6,5,4], // top /* [5,6,2,1], // right [6,7,3,2], // back */ [7,4,0,3]]; // left

Mis-ordered faces

 * Example 3 a more complex polyhedron with mis-ordered faces

When you select 'Thrown together' from the view menu and compile the design (not compile and render!) you will see a preview with the mis-oriented polygons highlighted. Unfortunately this highlighting is not possible in the OpenCSG preview mode because it would interfere with the way the OpenCSG preview mode is implemented.)

Below you can see the code and the picture of such a problematic polyhedron, the bad polygons (faces or compositions of faces) are in pink.

A correct polyhedron would be the following:

Beginner's tip:

If you don't really understand "orientation", try to identify the mis-oriented pink faces and then permute the references to the points vectors until you get it right. E.g. in the above example, the third triangle ([0,4,5]) was wrong and we fixed it as [4,0,5]. In addition, you may select "Show Edges" from the "View Menu", print a screen capture and number both the points and the faces. In our example, the points are annotated in black and the faces in blue. Turn the object around and make a second copy from the back if needed. This way you can keep track.

Clockwise Technique:

Orientation is determined by clockwise indexing. This means that if you're looking at the triangle (in this case [4,0,5]) from the outside you'll see that the path is clockwise around the center of the face. The winding order [4,0,5] is clockwise and therefore good. The winding order [0,4,5] is counter-clockwise and therefore bad. Likewise, any other clockwise order of [4,0,5] works: [5,4,0] & [0,5,4] are good too. If you use the clockwise technique, you'll always have your faces outside (outside of OpenSCAD, other programs do use counter-clockwise as the outside though).

Think of it as a Left Hand Rule:

If you hold the face and the fingers of your hand curls is the same order as the points, then your thumb points outwards.



Succinct description of a 'Polyhedron'

* Points define all of the points/vertices in the shape. * Faces is a list of flat polygons that connect up the points/vertices.

Each point, in the point list, is defined with a 3-tuple x,y,z position specification. Points in the point list are automatically given an identifier starting at zero for use in the faces list (0,1,2,3,... etc).

Each face, in the faces list, is defined by selecting 3 or more of the points (using the point identifier) out of the point list.

e.g. faces=[ [0,1,2] ] defines a triangle from the first point (points are zero referenced) to the second point and then to the third point.

When looking at any face from the outside, the face must list all points in a clockwise order.

Alternate Face Descriptions
Before 2014.03, faces could only be described via triangles. Since 2014.03, a face description can have any number of points. The points, all in the same plane, must be listed in the proper order.

An alternate (correct) face definition for example 3:

faces = [ [0,3,2,1], [0,1,5,4],  [2,3,4,5],    // outside [6,7,8,9], [7,6,10,11], [11,10,9,8], // inside [0,4,3,0,6,9,10,6],                  // front [1,2,5,1,7,11,8,7]                   // back ]

OpenSCAD/Primitive_solidi Руководство_пользователя_по_OpenSCAD/Примитивы_объемных_тел