Curved PN triangles

By Alex Vlachos, J. Peters, Chas. Boyd, Jason L. Mitchell. ACM Symposium on Interactive 3D Graphics and Games, 2001

323 citations recorded by the source corpus.

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Shape optimization with a level set based mesh evolution method (2014, unknown): “In our setting, as suggested in [65], this piece of surface is parametrized as a cubic Bézier patch σ : T → Γ, which interpolates the three vertices of T , together with the three associated normal vectors.”
Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems (2014, background): “In [46], the authors propose to take, for instance, b2,1,0 as the orthogonal projection over Ta0∂Ω of point a0 + (a1 −a0)/3.”
Isotropic Remeshing of Surfaces: A Local Parameterization Approach (2003, unknown): “[37] presented a simple and efficient, yet robust and accurate, method to construct such curved patches called PN triangles.”
Geometry clipmaps: terrain rendering using nested regular grids (2004, background): “For faithful shading, the normal map has twice the resolution of the geometry, since one normal per vertex is too blurry [Vlachos et al 2001].”
Recent Advances in Remeshing of Surfaces (2008, methodology): “, by using triangular cubic Bzier patches such as PN triangles [85] or continuous patches [88]).”