POLYGONAL_SURFACE
Two Files Defining a Polygonal Surface

These are some examples of POLYGONAL_SURFACE data, which can be thought of as a surface composed of polygonal faces. The polygons must all be of the same type (triangles, quadrilaterals or whatever).

If the polygons are of higher order than triangles, the user must take care that the vertices of each polygon all lie in a plane. Otherwise, no planar polygon will pass through the vertices. If the nonplanarity is significant, then the display will not look right at all.

The information defining the polygonal surface can be stored in two simple files:

• the node file lists a set of (x,y,z) values, which are vertices of the polygons.
• the face file lists, for each polygonal face, the indices of the nodes that form its vertices. These nodes are generally listed in a "counterclockwise" order, that is, they would be seen as being counterclockwise to an observer from the "outside" or "top" of the surface.

Related Data and Programs:

BEZIER_SURFACE is a data directory which describes Bezier surfaces and a file format for storing them.

FEM is a format used to store a finite element model. It includes a node and element file, as well as a node data file.

FEMPACK is a library of routines for working with finite element models. It includes routines to create a polygonal surface model of a sphere. It is available in a C++ version and a FORTRAN90 version and a MATLAB version.

MESH_BANDWIDTH is an interactive executable program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension. It is available in a C++ version and a FORTRAN90 version and a MATLAB version.

POLYGONAL_SURFACE_DISPLAY is an executable MATLAB program which can read in a polygonal surface dataset and display the data.

TABLE is a format used for both the node and face files.

TRIANGULATION_ORDER3 is a data directory which describes the related idea of a linear triangulation in which each triangle is defined by 3 nodes.

TRIANGULATION_ORDER6 is a data directory which describes the related idea of a quadratic triangulation in which each triangle is defined by 6 nodes.

Reference:

1. Edward Angel,
   Interactive Computer Graphics, a Top-Down Approach with OpenGL,
   Addison-Wesley, 2000.

Sample Polygonal Surface Datasets:

SPHERE_Q4 is a sphere, tiled with an 8 by 8 array of logically rectangular patches. The dataset was created by the sample calling program for FEMPACK and the image is a snapshot of the 3D display created by POLYGONAL_SURFACE_DISPLAY.

• sphere_q4_nodes.txt, the node file;
• sphere_q4_faces.txt, the face file;
• sphere_q4.png, a PNG image of the shape.

SPHERE_T3 is a sphere, tiled with an 8 by 8 array of logically triangular patches. The dataset was created by the sample calling program for FEMPACK and the image is a snapshot of the 3D display created by POLYGONAL_SURFACE_DISPLAY.

• sphere_t3_nodes.txt, the node file;
• sphere_t3_faces.txt, the face file;
• sphere_t3.png, a PNG image of the shape.

TETRA_T6 is a tetrahedron The dataset was created by hand. The image is a snapshot of the 3D display created by POLYGONAL_SURFACE_DISPLAY.

• tetra_t6_nodes.txt, the file of 10 nodes.
• tetra_t6_faces.txt, the file of 4 faces, each a 6-node triangle.
• tetra_t6.png, a PNG image of the shape.

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