How to draw a spherical triangle on a sphere in 3D?

Question

Suppose you know three vertices for a spherical triangle. Then how do you draw sides on a sphere in 3D?

I need python code for use in Blender 3d modeling software.

I already have a sphere made in 3D in Blender.

Thanks and happy blending.

note 1:

i have 3 points / vertices (p1, p2, p3) on a sphere for a spherical triangle but I need to trace the edges on the sphere in 3D

So, what would be the equations needed to determine all the vertices between each point of a pair of triangles on the sphere 3 edges from p1 to p2 - p2 to p3 and o3 to p1

I know that this has something to do with the Great Circle for geodesics on a sphere but cannot find the correct equations for calculating in spherical coordinates!

thank

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Answer 1

Python Blender:

import math
import Blender
from Blender import NMesh

x = -1 * math.pi

mesh = NMesh.GetRaw()
vNew = NMesh.Vert( x, math.sin( x ), 0 )
mesh.verts.append( vNew )

while x < math.pi:
 x += 0.1
 vOld = vNew
 vNew = NMesh.Vert( x, math.sin( x ), 0 )
 mesh.verts.append( vNew )
 mesh.addEdge( vOld, vNew )

NMesh.PutRaw( mesh, "SineWave", 1 )
Blender.Redraw()

: http://davidjarvis.ca/blender/tutorial-04.shtml

, :

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, :

• P ₁= (x ₁, y ₁, z ₁)
• P ₂= (x ₂, y ₂, z ₂)

, P ₁ P ₂ :

• :

  
  R = sqrt( x12 + y12 + z12 )
  

• (_m) P ₁ P ₂:

  
  Pm = (xm, ym, zm)
  xm = (x1 + x2) / 2
  ym = (y1 + y2) / 2
  zm = (z1 + z2) / 2

• P ₁ P ₂:

  
  Lm = sqrt( xm2, ym2, zm2 )

• :

  
  k = R / Lm

• :

  
  Am = k * Pm = (k * xm, k * ym, k * zm)

P ₁ P ₂ :

• P ₁ A _m
• A _m P ₂

. , P ₁ A _m A _m P ₂. , .

, , , () . , (, 0,01 ).

Spline

spline :

• (, )
• P < > 1 >
• < > >
• P < > 2 >

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Blender Artists

Blender , ; .

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http://www.mathnews.uwaterloo.ca/Issues/mn11106/DotProduct.php

http://cr4.globalspec.com/thread/27311/Urgent-Midpoint-of-Arc-formula

Answer 2

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