2.4.2.6 Triangle and Smooth Triangle
The triangle primitive is available in order to make more complex objects than the built-in shapes
will permit. Triangles are usually not created by hand but are converted from other files or generated by utilities. A
triangle is defined by
TRIANGLE:
triangle
{
<Corner_1>, <Corner_2>, <Corner_3>
[OBJECT_MODIFIER...]
}
where <Corner_n> is a vector defining the x, y, z coordinates of each corner of the
triangle.
Because triangles are perfectly flat surfaces it would require extremely large numbers of very small triangles to
approximate a smooth, curved surface. However much of our perception of smooth surfaces is dependent upon the way
light and shading is done. By artificially modifying the surface normals we can simulate a smooth surface and hide the
sharp-edged seams between individual triangles.
The smooth_triangle primitive is used for just such purposes. The smooth
triangles use a formula called Phong normal interpolation to calculate the surface normal for any point on the
triangle based on normal vectors which you define for the three corners. This makes the triangle appear to be a smooth
curved surface. A smooth triangle is defined by
SMOOTH_TRIANGLE:
smooth_triangle
{
<Corner_1>, <Normal_1>, <Corner_2>,
<Normal_2>, <Corner_3>, <Normal_3>
[OBJECT_MODIFIER...]
}
where the corners are defined as in regular triangles and <Normal_n> is a vector
describing the direction of the surface normal at each corner.
These normal vectors are prohibitively difficult to compute by hand. Therefore smooth triangles are almost always
generated by utility programs. To achieve smooth results, any triangles which share a common vertex should have the
same normal vector at that vertex. Generally the smoothed normal should be the average of all the actual normals of
the triangles which share that point.
The mesh object is a way to combine many triangle and smooth_triangle
objects together in a very efficient way. See "Mesh" for details.
More about "Mesh"
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