User:LABoyd2/polyhedron 160302

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polyhedron[edit | edit source]

Create a polyhedron with a list of points and a list of faces. The point list is all the vertices of the shape, the faces list is how the points relate to the surfaces of the polyhedron.

note: if your version of OpenSCAD is lower than 2014.03 replace "faces" with "triangles" in the below examples


vector of points or vertices (each a 3 vector).
(deprecated in version 2014.03, use faces) vector of point triplets (each a 3 number vector). Each number is the 0-indexed point number from the point vector.
(introduced in version 2014.03) vector of point n-tuples with n >= 3. Each number is the 0-indexed point number from the point vector. That is, faces=[[0,1,4]] specifies a triangle made from the first, second, and fifth point listed in points. When referencing more than 3 points in a single tuple, the points must all be on the same plane.
Integer. The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering.

Syntax example

 polyhedron(points = [ [x, y, z], ... ], faces = [ [p1, p2, p3..], ... ], convexity = N);

Point ordering for faces When looking at the face from the outside inwards, the points must be clockwise. You can rearrange the order of the points or the order they are referenced in each tuple. The order of faces is immaterial. Note that if your polygons are not all oriented the same way OpenSCAD will either print an error or crash completely, so pay attention to the vertex ordering. Again, remember that the 'pN' components of the faces vector are 0-indexed references to the elements of the points vector.

Example, a square base pyramid:

  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
A simple polyhedron, square based pyramid

polyhedron - polygon orientation issues[edit | edit source]

An example of a more complex polyhedron, and showing how to fix polyhedrons with badly oriented polygons.

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.

// Bad polyhedron
    (points = [
	       [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], 
	       [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50]
     faces = [
		  [0,2,3],   [0,1,2],  [0,4,5],  [0,5,1],   [5,4,2],  [2,4,3],
                  [6,8,9],  [6,7,8],  [6,10,11], [6,11,7], [10,8,11],
		  [10,9,8], [0,3,9],  [9,0,6], [10,6, 0],  [0,4,10],
                  [3,9,10], [3,10,4], [1,7,11],  [1,11,5], [1,7,8],  
                  [1,8,2],  [2,8,11], [2,11,5]
Polyhedron with badly oriented polygons

A correct polyhedron would be the following:

    (points = [
	       [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], 
	       [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50]
     faces = [
		  [0,3,2],  [0,2,1],  [4,0,5],  [5,0,1],  [5,2,4],  [4,2,3],
                  [6,8,9],  [6,7,8],  [6,10,11],[6,11,7], [10,8,11],
		  [10,9,8], [3,0,9],  [9,0,6],  [10,6, 0],[0,4,10],
                  [3,9,10], [3,10,4], [1,7,11], [1,11,5], [1,8,7],  
                  [2,8,1],  [8,2,11], [5,11,2]

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.

Polyhedron with badly oriented polygons

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.