Jump to content

Second order Barycentric interpolation


Recommended Posts

I already know that if I have a triangle with vertices v0, v1, v2 in property p0, p1, p2  then the property linearly interpolated at location l = a*p+ b*p1+(1-a-b)*p2

a=(area of triangle formed by the points v1, vand l)  / (area of the triangle formed by points v0, v1, v2)  

b= (area of triangle formed by the points v0, v2, and l) / (area of the triangle formed by points v0, v1, v2)  

My question is how do I generalize this to a higher order interpolation method? In my problem the property p = the normal vector to a surface and I have already calculated the Gaussian curvature of the surface to decide whether to subdivide the triangle into more triangles, but I don't want the second-order partial derivatives to go to waste.  

Link to comment
Share on other sites

Bump. 

 

Instead of interpolating the normal factors I could interpolate a function of the normal vectors such as diffuse and specular lighting which is still a function of second-order partial derivatives but the question is still the same.  If I have a property that is a function of the u, v parameters of a surface, and I also have the rate of change of the function I am trying to interpolate then how do I factor in the rate of change at the vertices of a triangle as well as the properties of the triangle at the vertices?

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.