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Geometry.rb
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Geometry.rb
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# Ref.: og_geometry.c (OpenGLUT) and freeglut_geometry.c (freeglut)
def generate_circle_table(n)
sint = nil
cost = nil
size = n.abs
angle = 2 * Math::PI / ((n == 0) ? 1 : n).to_f
sint = Array.new(size + 1) { 0.0 }
cost = Array.new(size + 1) { 0.0 }
size.times do |i|
sint[i] = Math.sin(angle * i)
cost[i] = Math.cos(angle * i)
end
sint[size] = sint[0]
cost[size] = cost[0]
return sint, cost
end
def geomSolidTorus(inner_radius, outer_radius, sides, rings) # Ref.: glutSolidTorus
sides += 1
rings += 1
vertex = Array.new(3 * sides * rings) { 0.0 }
normal = Array.new(3 * sides * rings) { 0.0 }
delta_psi = 2.0 * Math::PI / (rings - 1).to_f
delta_phi = -2.0 * Math::PI / (sides - 1).to_f
psi = 0.0
rings.times do |j|
cpsi = Math.cos(psi)
spsi = Math.sin(psi)
phi = 0.0
sides.times do |i|
offset = 3 * (j * sides + i)
cphi = Math.cos(phi)
sphi = Math.sin(phi)
vertex[offset + 0] = cpsi * (outer_radius + cphi * inner_radius)
vertex[offset + 1] = spsi * (outer_radius + cphi * inner_radius)
vertex[offset + 2] = sphi * inner_radius
normal[offset + 0] = cpsi * cphi
normal[offset + 1] = spsi * cphi
normal[offset + 2] = sphi
phi += delta_phi
end
psi += delta_psi
end
GL.Begin(GL::QUADS)
(sides-1).times do |i|
(rings-1).times do |j|
offset = 3 * (j * sides + i)
GL.Normal3dv(normal[offset, 3].pack('D3'))
GL.Vertex3dv(vertex[offset, 3].pack('D3'))
GL.Normal3dv(normal[offset+3, 3].pack('D3'))
GL.Vertex3dv(vertex[offset+3, 3].pack('D3'))
GL.Normal3dv(normal[offset+3*sides+3, 3].pack('D3'))
GL.Vertex3dv(vertex[offset+3*sides+3, 3].pack('D3'))
GL.Normal3dv(normal[offset+3*sides, 3].pack('D3'))
GL.Vertex3dv(vertex[offset+3*sides, 3].pack('D3'))
end
end
GL.End()
end
def geomSolidCone(base, height, slices, stacks) # Ref.: glutSolidCone
height = height.to_f
base = base.to_f
# Step in z and radius as stacks are drawn.
z_step = height / ((stacks > 0) ? stacks : 1).to_f
r_step = base / ((stacks > 0) ? stacks : 1).to_f
# Scaling factors for vertex normals
cosn = (height / Math.sqrt(height*height + base*base))
sinn = (base / Math.sqrt(height*height + base*base))
# Pre-computed circle
sint, cost = generate_circle_table(-slices)
# Cover the circular base with a triangle fan...
z0 = 0.0
z1 = z_step
r0 = base
r1 = r0 - base
GL.Begin(GL::TRIANGLE_FAN)
GL.Normal3d(0.0, 0.0, -1.0)
GL.Vertex3d(0.0, 0.0, z0)
(slices+1).times do |j|
GL.Vertex3d(cost[j] * r0, sint[j] * r0, z0)
end
GL.End()
# Cover each stack with a quad strip, except the top stack
(stacks-1).times do |i|
GL.Begin(GL::QUAD_STRIP)
(slices+1).times do |j|
GL.Normal3d(cost[j]*cosn, sint[j]*cosn, sinn)
GL.Vertex3d(cost[j]*r0, sint[j]*r0, z0)
GL.Vertex3d(cost[j]*r1, sint[j]*r1, z1)
end
z0 = z1
z1 += z_step
r0 = r1
r1 -= r_step
GL.End()
end
# The top stack is covered with individual triangles
GL.Begin(GL::TRIANGLES)
GL.Normal3d(cost[0]*cosn, sint[0]*cosn, sinn)
slices.times do |j|
GL.Vertex3d(cost[j+0]*r0, sint[j+0]*r0, z0 )
GL.Vertex3d(0, 0, height)
GL.Normal3d(cost[j+1]*cosn, sint[j+1]*cosn, sinn )
GL.Vertex3d(cost[j+1]*r0, sint[j+1]*r0, z0 )
end
GL.End();
end
def geomSolidCube(size) # Ref.: glutSolidCube
s = size * 0.5
GL.Begin(GL::QUADS)
GL.Normal3d(1.0, 0.0, 0.0)
GL.Vertex3d(+s,-s,+s); GL.Vertex3d(+s,-s,-s); GL.Vertex3d(+s,+s,-s); GL.Vertex3d(+s,+s,+s)
GL.Normal3d(0.0, 1.0, 0.0)
GL.Vertex3d(+s,+s,+s); GL.Vertex3d(+s,+s,-s); GL.Vertex3d(-s,+s,-s); GL.Vertex3d(-s,+s,+s)
GL.Normal3d(0.0, 0.0, 1.0)
GL.Vertex3d(+s,+s,+s); GL.Vertex3d(-s,+s,+s); GL.Vertex3d(-s,-s,+s); GL.Vertex3d(+s,-s,+s)
GL.Normal3d(-1.0, 0.0, 0.0)
GL.Vertex3d(-s,-s,+s); GL.Vertex3d(-s,+s,+s); GL.Vertex3d(-s,+s,-s); GL.Vertex3d(-s,-s,-s)
GL.Normal3d(0.0, -1.0, 0.0)
GL.Vertex3d(-s,-s,+s); GL.Vertex3d(-s,-s,-s); GL.Vertex3d(+s,-s,-s); GL.Vertex3d(+s,-s,+s)
GL.Normal3d(0.0, 0.0, -1.0)
GL.Vertex3d(-s,-s,-s); GL.Vertex3d(-s,+s,-s); GL.Vertex3d(+s,+s,-s); GL.Vertex3d(+s,-s,-s)
GL.End()
end
def geomSolidSphere(radius, slices, stacks) # Ref.: glutSolidSphere
# Pre-computed circle
sint1, cost1 = generate_circle_table(slices)
sint2, cost2 = generate_circle_table(stacks * 2)
slices = slices.abs
stacks = stacks.abs
# The top stack is covered with a triangle fan
z0 = 1.0
z1 = cost2[stacks > 0 ? 1 : 0]
r0 = 0.0
r1 = sint2[stacks > 0 ? 1 : 0 ]
GL.Begin(GL::TRIANGLE_FAN)
GL.Normal3d(0.0, 0.0, 1.0)
GL.Vertex3d(0.0, 0.0, radius)
slices.downto(0) do |j|
GL.Normal3d(cost1[j] * r1, sint1[j] * r1, z1 )
GL.Vertex3d(cost1[j] * r1 * radius, sint1[j] * r1 * radius, z1 * radius)
end
GL.End()
# Cover each stack with a quad strip, except the top and bottom stacks
(1...stacks).each do |i|
z0 = z1
z1 = cost2[i+1]
r0 = r1
r1 = sint2[i+1]
GL.Begin(GL::QUAD_STRIP)
(slices + 1).times do |j|
GL.Normal3d(cost1[j] * r1, sint1[j] * r1, z1 )
GL.Vertex3d(cost1[j] * r1 * radius, sint1[j] * r1 * radius, z1 * radius)
GL.Normal3d(cost1[j] * r0, sint1[j] * r0, z0 )
GL.Vertex3d(cost1[j] * r0 * radius, sint1[j] * r0 * radius, z0 * radius)
end
GL.End()
end
# The bottom stack is covered with a triangle fan
z0 = z1
r0 = r1
GL.Begin(GL::TRIANGLE_FAN)
GL.Normal3d(0.0, 0.0, -1.0)
GL.Vertex3d(0.0, 0.0, -radius)
(0..slices).each do |j|
GL.Normal3d(cost1[j] * r0, sint1[j] * r0, z0 )
GL.Vertex3d(cost1[j] * r0 * radius, sint1[j] * r0 * radius, z0 * radius)
end
GL.End()
end
def geomSolidDodecahedron() # Ref.: glutSolidDodecahedron
=begin
Magic Numbers: It is possible to create a dodecahedron by attaching
two pentagons to each face of of a cube. The coordinates of the points
are:
{(+/- x, 0, z), (+/- 1, 1, 1), (0, z, x)}
where x = (-1 + sqrt(5))/2 and z = (1 + sqrt(5))/2 or, approximately
x = 0.61803398875 and z = 1.61803398875.
=end
GL.Begin(GL::POLYGON)
GL.Normal3d(0.0, 0.525731112119, 0.850650808354)
GL.Vertex3d(0.0, 1.61803398875, 0.61803398875)
GL.Vertex3d(-1.0, 1.0, 1.0)
GL.Vertex3d(-0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(1.0, 1.0, 1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.0, 0.525731112119, -0.850650808354)
GL.Vertex3d(0.0, 1.61803398875, -0.61803398875)
GL.Vertex3d(1.0, 1.0, -1.0)
GL.Vertex3d(0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(-0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(-1.0, 1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.0, -0.525731112119, 0.850650808354)
GL.Vertex3d(0.0, -1.61803398875, 0.61803398875)
GL.Vertex3d(1.0, -1.0, 1.0)
GL.Vertex3d(0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(-0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(-1.0, -1.0, 1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.0, -0.525731112119, -0.850650808354)
GL.Vertex3d(0.0, -1.61803398875, -0.61803398875)
GL.Vertex3d(-1.0, -1.0, -1.0)
GL.Vertex3d(-0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(1.0, -1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.850650808354, 0.0, 0.525731112119)
GL.Vertex3d(0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(1.0, -1.0, 1.0)
GL.Vertex3d(1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(1.0, 1.0, 1.0)
GL.End()
GL.Begin (GL::POLYGON)
GL.Normal3d(-0.850650808354, 0.0, 0.525731112119)
GL.Vertex3d(-0.61803398875, 0.0, 1.61803398875)
GL.Vertex3d(-1.0, 1.0, 1.0)
GL.Vertex3d(-1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(-1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(-1.0, -1.0, 1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.850650808354, 0.0, -0.525731112119)
GL.Vertex3d(0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(1.0, 1.0, -1.0)
GL.Vertex3d(1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(1.0, -1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(-0.850650808354, 0.0, -0.525731112119)
GL.Vertex3d(-0.61803398875, 0.0, -1.61803398875)
GL.Vertex3d(-1.0, -1.0, -1.0)
GL.Vertex3d(-1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(-1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(-1.0, 1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.525731112119, 0.850650808354, 0.0)
GL.Vertex3d(1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(1.0, 1.0, -1.0)
GL.Vertex3d(0.0, 1.61803398875, -0.61803398875)
GL.Vertex3d(0.0, 1.61803398875, 0.61803398875)
GL.Vertex3d(1.0, 1.0, 1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(0.525731112119, -0.850650808354, 0.0)
GL.Vertex3d(1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(1.0, -1.0, 1.0)
GL.Vertex3d(0.0, -1.61803398875, 0.61803398875)
GL.Vertex3d(0.0, -1.61803398875, -0.61803398875)
GL.Vertex3d(1.0, -1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(-0.525731112119, 0.850650808354, 0.0)
GL.Vertex3d(-1.61803398875, 0.61803398875, 0.0)
GL.Vertex3d(-1.0, 1.0, 1.0)
GL.Vertex3d(0.0, 1.61803398875, 0.61803398875)
GL.Vertex3d(0.0, 1.61803398875, -0.61803398875)
GL.Vertex3d(-1.0, 1.0, -1.0)
GL.End()
GL.Begin(GL::POLYGON)
GL.Normal3d(-0.525731112119, -0.850650808354, 0.0)
GL.Vertex3d(-1.61803398875, -0.61803398875, 0.0)
GL.Vertex3d(-1.0, -1.0, -1.0)
GL.Vertex3d(0.0, -1.61803398875, -0.61803398875)
GL.Vertex3d(0.0, -1.61803398875, 0.61803398875)
GL.Vertex3d(-1.0, -1.0, 1.0)
GL.End()
end