r - Plotting surfaces with contour map in 3D over triangles

The example code here for rgl does almost what I want. However my (x,y) are not in a rectangle but in a triangle that is half of the rectangle (x=0..1, y=0..1 and z is missing if x+y>1). My input

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r - Plotting surfaces with contour map in 3D over triangles - Stack Overflow

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r - Adding Contour Lines to 3D Plots - Stack Overflow

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r - Adding Contour Lines to 3D Plots - Stack Overflow

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