Global constrained parameterization of triangulated surfaces

• US 6,300,958 B1
• Filed: 07/17/1998
• Issued: 10/09/2001
• Est. Priority Date: 07/17/1998
• Status: Expired due to Fees

• Current Assignee: T-Surf, S.A.
• Original Assignee: T-Surf Corporation
• Inventors: Mallet, Jean-Laurent
• Primary Examiner(s): Nguyen, Phu K.
• Application Number:
  US09/118,348
• Time in Patent Office: 1,180 Days
• Field of Search: 345/430, 345/428, 345/419, 345/440, 345/441, 345/442, 345/443
• US Class Current: 345/442
• CPC Class Codes: G06T 15/04 Texture mapping
• CPC Class Codes: G06T 17/20 Finite element generation, e.g. wire-frame surface description, tesselation

Abstract

Methods and apparatus for mapping a feature onto a simulated surface having contoured portions, the surface being definable by a plurality of generally adjacent triangulations, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface. In one embodiment, the isoparametric curves are characterized in that when the surface is flat, the isoparametric curves intersect one another in a perpendicular manner, and the perpendicularity of the intersections on the contoured portions of the surface is maintained. In another embodiment, the isoparametric curves are characterized in that when the surface is flat. The isoparametric curves are spaced a predetermined distance apart, and the spacing of the intersections on the contoured portions of the surface is maintained. In a third embodiment of the invention, the isoparametric curves are characterized by defined mathematical relationships having a plurality of variables associated with at least the topology of the surface, and at least one of the variables is held constant between isoparametric curves. Preferably, each of the triangulations are characterized by vertices terminating at points on the surface, and the method further includes using the vertices to define a gradient of a mathematical function associated with the feature, which function is interpolated over the triangulated surface.

Claims

1. Method for mapping a feature onto a simulated surface having contoured portions. The surface being definable by a plurality of generally adjacent triangulations defining border nodes and internal nodes on the surface, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface, the isoparametric curves characterized in that when the surface is flat, the isoparametric curves intersect one another in a perpendicular manner at least at points proximate to at least some of the internal nodes, the method comprising maintaining the perpendicularity of the intersections of at least some of the isoparametric curves proximate to at least some of the internal nodes on the contoured portions of the surface.

2. Method for mapping a feature onto a simulated surface having contoured portions, the surface being definable by a plurality of generally adjacent triangulations, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface, the isoparametric curves characterized in that when the surface is flat, the isoparametric curves are spaced a predetermined distance apart, the method comprising maintaining the predetermined spaced distance between at least some of the isoparametric curves on the contoured portions of the surface.

3. Method for mapping a feature onto a simulated surface, the surface being definable by a plurality of generally adjacent triangulations, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface, the surface characterized by a defined secondary isoparametric curve projected onto the surface, the method comprising aligning at least one of the plurality of isoparametric curves to be coincident with the defined secondary isoparametric curve.

4. Method for mapping a feature onto a simulated surface having contoured portions, the surface being definable by a plurality of generally adjacent triangulations, each triangulation be defined by vertices terminating at points on the surface, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface, the surface being characterized by a linear discontinuity such that a point on the surface along the discontinuity may be identified with two vertices of non-adjacent triangulations, the method comprising maintaining the identified value of the feature associated with a point on the surface along the discontinuity at the two both vertices.

5. Method for mapping a feature onto a simulated surface having contoured portions, the surface being definable by a plurality of generally adjacent triangulations, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface, the isoparametric curves characterized by defined mathematical relationships comprising a plurality of variables associated with at least the topology of the surface, the method comprising holding at least one of the variables constant between isoparametric curves.

6. The method of claim 5 wherein each of the triangulations are characterized by vertices terminating at points on the surface, and wherein the method further comprises using the vertices to define a gradient of a mathematical function associated with the feature, which function is interpolated over the triangulated surface.

7. The method of claim 5 wherein the at least one variable is held constant to constrain the mapping of the values of the feature according to the equation $\begin{array}{c}\sum _{}\end{array}$

α



 



ε



 



Ω



{Acv

(α

)·

ϕ

v

(α

)}=bcv(10)

wherein α

ε

Ω

defines a set of the vertices, ν

ε

{u, v}, {u, v} being associated with coordinates for an identifiable feature value, φ

^ν

is a discrete gradient function associating the vertices with the feature to be mapped to the surface, and the values A_cv(α

) and the scalar b_cv are constant given coefficients defining the constraint c.

8. The method of claim 6 further comprising the step of displaying the simulated surface.

9. An apparatus for generating a simulated topological surface having contoured portions and a feature mapped thereon, comprising a memory and a processor, wherein the surface is defined by surface database stored in the memory and representing a plurality of generally adjacent triangles having vertices and points at the vertices, and wherein the processor is configured to perform a series of computer executable steps, the steps comprising associating a feature value from a data base of feature values stored in the memory with ones of the points on the surface, defining a plurality of intersecting isoparametric curves linking identified feature values to identified points on the surface, the isoparametric curves characterized by defined mathematical relationships comprising a plurality of variables associated with at least the topology of the surface, holding at least one of the variables constant between isoparametric curves, and generating a representation of the surface having feature values constrained to the surface according to the isoparametric curves, and saving the representation in the computer memory.