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

15.2: Plot 3D Surface and Contour Plots - Engineering LibreTexts

raster - Create a 3D topographic map with locations marked on the map using R - Geographic Information Systems Stack Exchange

Creating 3D Plots in R Programming - persp() Function - GeeksforGeeks

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15.2: Plot 3D Surface and Contour Plots - Engineering LibreTexts

Transform ggplot2 objects into 3D — plot_gg • rayshader