This paper proposes a method to construct high-quality and compatible high-order surface meshes with bounded ap-proximation errors.Given two closed,oriented,and topologically equivalent surfaces and a sparse set of corresponding landmarks,the proposed method contains two steps:(1)generate compatible high-order meshes with bounded approximation errors and(2)re-duce mesh complexity while ensuring that approximation errors are always bounded,and reduce the distortion between the com-patible meshes and approximation errors with the original meshes by optimizing the control vertices.The first step is to generate compatible linear meshes with bounded approximation errors,and then upgrade them to high-order meshes.In the second step,the mesh complexity is effectively reduced by iteratively performing an edge-based remeshing and increasing the compatible target edge lengths.The Jacobian matrix of the mapping between 3D Bézier triangles is derived from tangent space,so that the distortion energy can be effectively optimized.By optimizing the distortion energy and approximation errors energy,the distortion between compatible meshes and approximation errors are effectively reduced.Tests on various pairs of complex models demonstrate the ef-ficacy and practicability of our method for constructing high-quality compatible high-order meshes with bounded approximation errors.
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