CODEWITHSUNDEEP
mathinterpolationfinite-element-analysis
Neg K
Neg K

Reputation: 27

An algorithm suggestion for interpolation in a 2d plane, when the plane is in 3D space

I'm trying to find value for a point within a triangle or square. By "value" I do not mean coordinates. Suppose there is a value (number) assigned to each node of the square/triangle. The square/triangle is on a plane. How can I interpolate values to find out the value of the point inside.

I don't want to try the bilinear interpolation since that requires for me to know exactly which plane we are in. This plane is not in x-y or y-z or x-z. This plane can be a sloped plane in 3D. (not warped)

Thank you in advance for the help.

Upvotes: 0

Views: 132

Answers (1)

MBo
MBo

Reputation: 80325

Any rectandle or triangle might be interpolated using one vertex (here A) and two vectors of adjacent sides (here AB = B - A, AC = C - A)

P(u, v) =  A + AB * u + AC * v

Parameters u,v lie in range 0..1, also for triangle their sum should not exceed 1

This representation is suitable for any plane orientation.

For reference:

 AB.x = B.x - A.x etc

 fourth vertex of rectangle is:
 D = A + AB * 1 + AC * 1
 middle of rectangle: 
 M =  A + AB * 0.5 + AC * 0.5

 middle of BC side in triangle:
 mBC = A + AB * 0.5 + AC * 0.5
 median intersection point in triangle:
 cT = A + AB * 0.5 * 2/3 + AC * 0.5 * 2/3

Upvotes: 1

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