Computing boundary continuity constraints for patching curve networks
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for receiving data describing a model, the model describing a curve network; determining boundary continuity constraints for each edge, of each face, in the model; combining the determined boundary continuity constraints to determine respective boundary continuity for each face; and determining, using the respective boundary continuity constraints, a respective surface patch for each face.
1. A method implemented by a computer-aided design (CAD) system comprising one or more computers, the method comprising:
receiving a model representing a three-dimensional object in the (CAD) system, the model including a plurality of edges of a curve network, wherein the curve network includes one or more closed loops of edges, and wherein each respective closed loop of edges in the curve network represents a respective face of the object;
determining, by the CAD system for a first end point of a particular edge of a face of the model, a first vector of a first adjacent edge of the face, wherein the first adjacent edge meets the particular edge at the first end point, and wherein the first vector represents an orientation of the first adjacent edge where the first adjacent edge meets the first end point of the particular edge;
determining, by the CAD system for a second end point of the particular edge of the face of the model, a second vector of a second adjacent edge of the face, wherein the second adjacent edge meets the particular edge at the second end point, and wherein the second vector represents an orientation of the second adjacent edge where the second adjacent edge meets the second end point of the particular edge;
generating, by the CAD system, a first derivative field including sweeping the first vector of the first adjacent edge along the particular edge between the first end point and the second end point;
generating, by the CAD system, a second derivative field including sweeping the second vector of the second adjacent edge along the particular edge between the first end point and the second end point; and
generating, by the CAD system, boundary continuity constraints for the particular edge of the face by applying a blending function to respective components of the first derivative field and the second derivative field to generate a blended derivative field defining the boundary continuity constraints for the particular edge.
2. The method of claim 1 , wherein the blending is performed using a linear function to achieve a G 0 continuity between the first and second adjacent edges.
3. The method of claim 1 , wherein the first vector and the second vector are tangent vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G′ continuity between the first adjacent edge and the second adjacent edge.
4. The method of claim 1 , wherein the first vector and the second vector are curvature vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G 2 continuity between the first adjacent edge and the second adjacent edge.
5. The method of claim 1 , wherein determining the boundary continuity constraints for the particular edge comprises determining the boundary continuity constraints using only local geometric information of the respective face.
6. A non-transitory computer storage medium having instructions stored thereon that, when executed by a computer-aided design (CAD) system comprising one or more computers, cause the CAD system to perform operations comprising:
receiving a model representing a three-dimensional object in the CAD system, the model including a plurality of edges of a curve network, wherein the curve network includes one or more closed loops of edges, and wherein each respective closed loop of edges in the curve network represents a respective face of the object;
determining, by the CAD system for a first end point of a particular edge of a face of the model, a first vector of a first adjacent edge of the face, wherein the first adjacent edge meets the particular edge at the first end point, and wherein the first vector represents an orientation of the first adjacent edge where the first adjacent edge meets the first end point of the particular edge;
determining, by the CAD system for a second end point of the particular edge of the face of the model, a second vector of a second adjacent edge of the face, wherein the second adjacent edge meets the particular edge at the second end point, and wherein the second vector represents an orientation of the second adjacent edge where the second adjacent edge meets the second end point of the particular edge;
generating, by the CAD system, a first derivative field including sweeping the first vector of the first adjacent edge along the particular edge between the first end point and the second end point;
generating, by the CAD system, a second derivative field including sweeping the second vector of the second adjacent edge along the particular edge between the first end point and the second end point; and
generating, by the CAD system, boundary continuity constraints for the particular edge of the face by applying a blending function to respective components of the first derivative field and the second derivative field to generate a blended derivative field defining the boundary continuity constraints for the particular edge.
7. The medium of claim 6 , wherein the blending is performed using a linear function to achieve a G 0 continuity between the first and second adjacent edges.
8. The medium of claim 6 , wherein the first vector and the second vector are tangent vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G′ continuity between the first and second adjacent edges.
9. The medium of claim 6 , wherein the first vector and the second vector are curvature vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G 2 continuity between the first adjacent edge and the second adjacent edge.
10. The medium of claim 6 , wherein determining the boundary continuity constraints for the particular edge comprises determining the boundary continuity constraints using only local geometric information of the respective face.
11. A computer-aided design (CAD) system comprising:
one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising:
receiving a model representing a three-dimensional object in the CAD system, the model including a plurality of edges of a curve network, wherein the curve network includes one or more closed loops of edges, and wherein each respective closed loop of edges in the curve network represents a respective face of the object;
determining, by the CAD system for a first end point of a particular edge of a face of the model, a first vector of a first adjacent edge of the face, wherein the first adjacent edge meets the particular edge at the first end point, and wherein the first vector represents an orientation of the first adjacent edge where the first adjacent edge meets the first end point of the particular edge;
determining, by the CAD system for a second end point of the particular edge of the face of the model, a second vector of a second adjacent edge of the face, wherein the second adjacent edge meets the particular edge at the second end point, and wherein the second vector represents an orientation of the second adjacent edge where the second adjacent edge meets the second end point of the particular edge;
generating, by the CAD system, a first derivative field including sweeping the first vector of the first adjacent edge along the particular edge between the first end point and the second end point;
generating, by the CAD system, a second derivative field including sweeping the second vector of the second adjacent edge along the particular edge between the first end point and the second end point; and
generating, by the CAD system, boundary continuity constraints for the particular edge of the face by applying a blending function to respective components of the first derivative field and the second derivative field to generate a blended derivative field defining the boundary continuity constraints for the particular edge.
12. The system of claim 11 , wherein the blending is performed using a linear function to achieve a G 0 continuity between the first and second adjacent edges.
13. The system of claim 11 , wherein the first vector and the second vector are tangent vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G 1 continuity between the first adjacent edge and the second adjacent edge.
14. The system of claim 11 , wherein the first vector and the second vector are curvature vectors, and wherein generating the blended derivative field for the particular edge comprises blending the first derivative field and the second derivative field to achieve a G 2 continuity between the first adjacent edge and the second adjacent edge.
15. The system of claim 11 , wherein determining the boundary continuity constraints for the particular edge comprises determining the boundary continuity constraints using only local geometric information of the respective face.
16. The method of claim 1 , wherein generating the boundary continuity constraints for the particular edge of the face comprises determining the boundary continuity constraints without solving a global system of the curve network.
17. The method of claim 1 , wherein generating the first derivative field comprises evaluating a plurality of derivatives using surface derivatives of the three-dimensional object.
18. The method of claim 1 , wherein blending the first derivative field and the second derivative field comprises applying a blending function that uses a same measure of continuity for each of the first derivative field and the second derivative field.
19. The computer storage medium of claim 6 , wherein generating the boundary continuity constraints for the particular edge of the face comprises determining the boundary continuity constraints without solving a global system of the curve network.
20. The computer storage medium of claim 6 , wherein generating the first derivative field comprises evaluating a plurality of derivatives using surface derivatives of the three-dimensional object.
21. The computer storage medium of claim 6 , wherein blending the first derivative field and the second derivative field comprises applying a blending function that uses a same measure of continuity for each of the first derivative field and the second derivative field.
22. The system of claim 11 , wherein generating the boundary continuity constraints for the particular edge of the face comprises determining the boundary continuity constraints without solving a global system of the curve network.
23. The system of claim 11 , wherein generating the first derivative field comprises evaluating a plurality of derivatives using surface derivatives of the three-dimensional object.
24. The system of claim 11 , wherein blending the first derivative field and the second derivative field comprises applying a blending function that uses a same measure of continuity for each of the first derivative field and the second derivative field.