| CPC G06T 19/20 (2013.01) [G06T 7/64 (2017.01); G06T 17/30 (2013.01); G06T 2219/2021 (2013.01)] | 20 Claims |

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1. A modeling system comprising:
at least one processor, communicatively coupled to non-volatile memory and instructions that, when executed by the processor, cause the processor to:
retrieve from the non-volatile memory a 3D virtual model of an object;
define a first parameter domain;
parameterize the 3D virtual model over the first parameter domain to thereby generate a parameterized surface representing the 3D virtual model;
identify one or more feature curves in the 3D virtual model;
project the one or more feature curves in the 3D virtual model into the first parameter domain of the parameterized surface to generate a plurality of two-dimensional curves in the first parameter domain of the parameterized surface;
define a second parameter domain;
construct a map, comprising horizontal map functions and vertical map functions, between the first parameter domain and the second parameter domain, according to which
an image of each projected feature curve is contained in a fixed value of a parameter domain variable of the second parameter domain; and
the map is invertible, and maps a boundary of the first parameter domain to a boundary of the second parameter domain;
compose an inverse of the horizontal map functions and the vertical map functions with the parameterized surface to obtain a reparameterized surface, wherein the inverse maps horizontal lines in the second parameter domain to horizontal feature curves in the first parameter domain and maps vertical lines in the second parameter domain to vertical feature curves in the first parameter domain; and
output the reparameterized surface.
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