c++: Find the closest point on a mesh to a query point - c++

Question

Here is what I need:
Given a point(x,y,z) in 3d space, and a mesh compose of some vertices(x,y,z), to calculate and return the close point coordinate on that mesh.
The function probably like this:
bool closePointOnMesh(const Point& queryPoint, const Mesh& myMesh, float maxDistance);
I have done some searching, and probably I will choose octree to reduce the calculation.
But there are still many details that I can't understand:
1: How the octree node been subdivided, so each node contains may contains 0~some triangles? It is easier to subdivided the cell further based on vertices and just store vertices directly.
2: How the octree structure helps to reduce the calculation, I know if the cell is empty I will just disregard it. But do I need to get all the closest point within each triangle face in a octree cell to the queryPoint, so I finally get the most closest point of all? that sound still heavy. Beside it will be more easier if I just iter through all the triangles, get the closest point from them, which means no need for the octree???
3: Is there a fast way to get the closest point to a point within a triangle face?
4: how the maxDistance limit helps to reduce the calculation?

Answer 1

For #3, here's some code on how to get the closest point of a triangle. It projects the point onto the triangle's plane, and then clamps the barycentric coordinates to [0,1], and uses those values computes the closest point.
Copied below:
vector3 closesPointOnTriangle( const vector3 *triangle, const vector3 &sourcePosition )
{
vector3 edge0 = triangle[1] - triangle[0];
vector3 edge1 = triangle[2] - triangle[0];
vector3 v0 = triangle[0] - sourcePosition;
float a = edge0.dot( edge0 );
float b = edge0.dot( edge1 );
float c = edge1.dot( edge1 );
float d = edge0.dot( v0 );
float e = edge1.dot( v0 );
float det = a*c - b*b;
float s = b*e - c*d;
float t = b*d - a*e;
if ( s + t < det )
{
if ( s < 0.f )
{
if ( t < 0.f )
{
if ( d < 0.f )
{
s = clamp( -d/a, 0.f, 1.f );
t = 0.f;
}
else
{
s = 0.f;
t = clamp( -e/c, 0.f, 1.f );
}
}
else
{
s = 0.f;
t = clamp( -e/c, 0.f, 1.f );
}
}
else if ( t < 0.f )
{
s = clamp( -d/a, 0.f, 1.f );
t = 0.f;
}
else
{
float invDet = 1.f / det;
s *= invDet;
t *= invDet;
}
}
else
{
if ( s < 0.f )
{
float tmp0 = b+d;
float tmp1 = c+e;
if ( tmp1 > tmp0 )
{
float numer = tmp1 - tmp0;
float denom = a-2*b+c;
s = clamp( numer/denom, 0.f, 1.f );
t = 1-s;
}
else
{
t = clamp( -e/c, 0.f, 1.f );
s = 0.f;
}
}
else if ( t < 0.f )
{
if ( a+d > b+e )
{
float numer = c+e-b-d;
float denom = a-2*b+c;
s = clamp( numer/denom, 0.f, 1.f );
t = 1-s;
}
else
{
s = clamp( -e/c, 0.f, 1.f );
t = 0.f;
}
}
else
{
float numer = c+e-b-d;
float denom = a-2*b+c;
s = clamp( numer/denom, 0.f, 1.f );
t = 1.f - s;
}
}
return triangle[0] + s * edge0 + t * edge1;
}