**comp.graphics.algorithms**

## Subject: **How to project a point onto a surface?**

This tricky problem is part of search of geodesic line. Suppose I have

a surface and I want to find out the geodesic line between two points

in the surface. This surface has curvature and is composed of many

triangular elements.

I choose two end points in the surface then I can generate a straight

line between these points. I divide this straight line into 5 or 6

segments. Now I want to project generated segment nodes onto the

surface. Firstly, the x and y co-ordinates of each of the segment nodes

are used to locate specific surface trangular element in which it lies.

The z co-ordinate of the segment node is determined using the known

nodal co-ordinates of the surface element by a standard shape function.

>From these initial positions, the projected segment nodes are allowed

to slide over the surface elements in search of the equilibrium

configuration. Once the final state of equilibrium is attained, the

path of a geodesic will be defined by these projected segment nodes.

My questions are

1) how to locate specific surface trangular element using the x and y

co-ordinates of each of the segment nodes? I know the node coordinates

of each surface triangular element but I don't know which element I

need locate.

2) how to work out the z co-ordinate of the segment node using the

known nodal co-ordinates of the surface element by a standard shape

function?

Any suggestion would be appreciated. Thanks.

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