CenterStage Object Class: Polyhedron Subclass of the Root class The Polyhedron class is one of the basic classes in CenterStage. It allows you to specify polyhedra by giving the the vertices and faces that make up the polyhedron. You can create lists of vertices, with optional names to use as a reference when creating the faces, and lists of faces constructed from these vertices, or you can simply give faces as lists of points. You can specify colors and other characteristics on a face-by-face basis, or for groups of faces. The Polyhedron class has two main directives: Vertices {vertex list} This specifies a list of vertices that you can use to define your faces. This is simply a list of vertices, and you refer to them by index (the first index is 0). Optionally, any vertex can be preceded by an identifying name ending in a colon. For example Vertices { (1,0,0) (0,1,0) (0,0,1) Origin: (0,0,0) } defines four vertices with indices 0, 1, 2, and 3, but the final vertex can also be referred to as "Origin". The vertices can include formulas or variables, for example: Vertices { (1,t,0) (0,1,t) (t,0,1) (1+t,0,t) (1-t,t,0) (t-1,0,0) } Before the vertex list is parsed, CenterStage performs variable substitution and command evaluation on it, so you can compute the vertex list via a procedure if you wish: Vertices {[myVertexList]} proc myVertexList {} { (compute list here) return \$vertices } Note that the braces around the square brackets are important as they postpone the procedure evaluation until the vertex list is actually needed. You could also use the Setup script to compute the vertex list and set the Vertices from a variable: Vertices {\$vertices} Setup { set vertices {} foreach i {0 1 2} { let V = XY(i*pi/3) * (1,0,1) lappend vertices \$V } } Here, the vertex list is created algorithmically: it consists of three different rotations of the vector (1,0,1). (The XY function is built into CenterStage, anc can be called from any object). Faces {face list} The face list, in its simplest form, is a list of pairs of indices into the vertex list, or names of vertices in the list. For example, given the points defined in the first example above, you could specify faces as follow: Faces { {Origin 0 1} {Origin 1 2} {Origin 0 2} {0 1 2} } This generates a tetrahedron using the four vertices. Note that faces can be made from any number of vertices. A face that is a single vertex will be shown as a dot, a face made from two vertices will be shown as a line, and other faces will be shown as filled polygons. For best results, all the vertices of a polygon should be coplanar. You can also inter-mix actual points with the indices and names, e.g.: Faces { {Origin 0 (-1,0,0)} {1 (0,-1,0)} {(1,1,1) (-1,-1,-1) (1,2,3)} } Any face can be followed by "<-" and a list of attributes for the face, as in Faces { {0 1 2} <- {color {1 .5 0} outline} } or a list of faces can be followed by attributes: Faces { {{0 1} {1 2} {2 3}} <- {color {0 0 0}} {{1 2 3} {0 2 3}} <- {outline} } The attributes include the following: solid polygonal faces should be filled in. outline polygonal faces should be shown as outlines only. width n the width for the face outline normalize the face color should be included in the color normalization process. noadjust the face color should not be normalized. color c specifies the color for the face: it is either an index into the color table or an RGB color specification. vcolors list specifies a list of color indices or RGB values that should be used as the colors for the vertices of the face. The list should have the same number of colors as the face has vertices.