Sphere trianglutaion

The first method - using latitude and longitudeSphere created using latitude and longitude

Compute points of the sphere using latitude and longitude.

If sphere centre is [a, b, c] and radius is r:

x = a + r * cos(θ) * cos(φ)

y = b + r * sin(φ)

z = c + r * sin(θ) * cos(φ)

θ ∈ <0, 2*π)

φ ∈ <0, π)

Pseudocode

a,b,c = sphere's centre
r = sphere radius
angle = angle of one step in degrees
r2 := 360 / angle
p2 := 180 / angle
for y := -r2 to r2 do
    cy  := cos(y*angle)
    cy1 := cos((y+1)*angle)
    sy  := sin(y*angle)
    sy1 := sin((y+1)*angle)
    for i := -p2 to p2 do
        ci := cos(i*angle)
        si := sin(i*angle)
        trianglePoint(a+r * ci*cy, b+r*sy, c+r * si*cy))
        trianglePoint(a+r * ci*cy1, b+r*sy1, c+r * si*cy1)
    forend
forend

Download executable, source code and project file for Code::Blocks

 

The second method - using subdivisionSphere created by subdivision

Pseudocode is for sphere with [0, 0, 0] centre. If you want your sphere to have different centre, just move the sphere you get from pseudocode.


T = set of cube's triangles
steps = subdivision steps
for i := 1 to steps do
    Tnew = {}
    for each t ∈ T do
        midab = (t.a + t.b)/2;
        midab = midab * length(t.a) / length(midab)
        tnew1 = triangle(t.a, t.c, midab)
        tnew2 = triangle(t.b, t.c, midab)
        add tnew1 to Tnew
        add tnew2 to Tnew
    forend
    T = Tnew
forend

Advantage of this method is a better distribution of triangles around the sphere's poles.

Download executable, source code and project file for Code::Blocks

You must press "s" multiple times in the beggining to get a sphere from a cube

Controls:

use mouse to rotate the sphere

press "w" - render wireframe model

press "f" - render solid model

press "s" - subdivide


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