Section21.12

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## 21.12 tetra.input

)set expose add con DenavitHartenbergMatrix Bring DH matrices into the
environment
x1:DFLOAT := sqrt(2.0@DFLOAT/3.0@DFLOAT) Set up the coordinates of the
x2:DFLOAT := sqrt(3.0@DFLOAT)/6 corners of the tetrahedron.
p1 := point [-0.5@DFLOAT, -x2, 0.0@DFLOAT] Some needed points
p2 := point [0.5@DFLOAT, -x2, 0.0@DFLOAT]
p3 := point [0.0@DFLOAT, 2*x2, 0.0@DFLOAT]
p4 := point [0.0@DFLOAT, 0.0@DFLOAT, x1]
baseTriangle := [p2, p1, p3] The base of the tetrahedron
mt := [0.5@DFLOAT*(p2+p1), 0.5@DFLOAT*(p1+p3), 0.5@DFLOAT*(p3+p2)]
The middle triangle inscribed
in the base of the tetrahedron
bt1 := [mt.1, p1, mt.2] The bases of the triangles of
bt2 := [p2, mt.1, mt.3] the subdivided tetrahedron
bt3 := [mt.2, p3, mt.3]
bt4 := [0.5@DFLOAT*(p2+p4), 0.5@DFLOAT*(p1+p4), 0.5@DFLOAT*(p3+p4)]
tt1 := tri2tri(baseTriangle, bt1) Create the transformations
tt2 := tri2tri(baseTriangle, bt2) that bring the base of the
tt3 := tri2tri(baseTriangle, bt3) tetrahedron to the bases of
tt4 := tri2tri(baseTriangle, bt4) the subdivided tetrahedron
drawPyramid(n) == Draw a Sierpinsky tetrahedron
s := createThreeSpace() with n levels of recursive
dh := rotatex(0.0@DFLOAT) subdivision
drawPyramidInner(s, n, dh)
makeViewport3D(s, "Sierpinsky Tetrahedron")
drawPyramidInner(s, n, dh) == Recursively draw a Sierpinsky
n = 0 => makeTetrahedron(s, dh, n) tetrahedron
drawPyramidInner(s, n-1, dh * tt1) Draw the 4 recursive pyramids
drawPyramidInner(s, n-1, dh * tt2)
drawPyramidInner(s, n-1, dh * tt3)
drawPyramidInner(s, n-1, dh * tt4)
makeTetrahedron(sp, dh, color) == Draw a tetrahedron into the
w1 := dh*p1 given space with the given
w2 := dh*p2 color, transforming it by
w3 := dh*p3 the given DH matrix
w4 := dh*p4
polygon(sp, [w1, w2, w4])
polygon(sp, [w1, w3, w4])
polygon(sp, [w2, w3, w4])
void()

Sierpinsky's Tetrahedron

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