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

Description

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

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

Three-Dimensional Plots (GNU Octave (version 9.1.0))

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

Heatmaps and different color maps for surface plot : r/geogebra

Plotting Surfaces with R · R Views

Help Online - Tutorials - 3D and Contour

Solved: Help in plotting the RSM contour plot similar to the output in MINITAB (jmp 17 - JMP User Community

Solved: Help in plotting the RSM contour plot similar to the output in MINITAB (jmp 17 - JMP User Community

How to activate contour lines in Mesh3D as in Surface3D? - 📊 Plotly Python - Plotly Community Forum

Help Online - Origin Help - Creating Contour Graphs

3D Plot in R Programming-Quick Guide

GNU Octave: Three-Dimensional Plots