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I attached a HeightField to a 2D curvilinear lattice, and when I change the scale from 0, the surface is distorted.
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This is a result of using a 2D curvilinear lattice with a HeightField. Keep the Scale at 0 for this type of lattice.

A HeightField offsets the surface in the direction perpendicular to the surface by an amount proportional to the scale factor times component value. This means higher elevations will be distorted more. The higher elevations at the peaks extend outwards more than the lower regions and ultimately start to intersect with each other. Also, the distortion direction is perpendicular to the curvilinear lattice, so the offset will be in a more horizontal direction than vertical along the sides of the hills.
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