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INTRODUCTION:

i have created application that splits triangles (2d simplex) and tetrahedrons (3d simplex) to

1 triangle -> 3 quadrilaterals

1 tetrahedron -> 4 bricks (8 nodal elements)

my application uses element center of gravity in both cases. and than splits.

for triangle new nodes are in

cogs of edges

cog of triangle

for tetrahedron new nodes are in

cogs of edges

cogs of triangles

cog of tetrahedron

as shown in these pictures:

http://img534.imageshack.us/img534/6105/triangleg.jpg [Broken]

http://img225.imageshack.us/img225/112/tetrahedron.jpg [Broken]

QUESTION:

i would like to have mathematical proof that all the new elements

case 1 - quadrilaterals

case 2 - bricks

are convex

when elements are splited in this way.

thank you for your interest very much

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# Simplex splitting using center of gravity

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