N-Sided Patch Generation from 3D Sketch Curves
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Solution Overview
Problem
Current 3D surface modeling techniques, such as polygon meshes and parametric representations, are limited in accurately representing curved surfaces and require complex manipulation of control vertices, while sketch-based modeling tools lack the ability to create sharp creases and complex surface features, especially in the interior of 3D models.
Innovation Solution
The development of an arbitrary-sided variational surface patch that interpolates a network of sketched curves, allowing for the creation of smooth and sharp features with G1 continuity, and user interface workflows that simplify the construction of complex 3D models by generating patches from closed 2D curves drawn on a 3D surface, enabling intuitive control over surface features like holes and internal constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If polygon meshes are used to represent 3D surfaces, then the representation is simple and easy to manipulate, but the accuracy of curved surfaces is poor and large numbers of control vertices are required
Solution Approach 1:
The patent transforms the control vertices from 3D spatial coordinates into 2D curve sketches on a reference surface. This parameter transformation reduces the complexity of controlling numerous 3D vertices while maintaining or improving curved surface accuracy, as the 2D curves serve as constraints that define the 3D surface geometry more efficiently
2Device complexity
If parametric representations such as NURBS are used, then a sparser set of control vertices is provided with smooth continuous surfaces, but the user must represent art as quadrilateral based patches with iso-parameter lines following principle curvatures
Solution Approach 1:
Instead of constraining the user to draw iso-parameter lines that follow principle curvatures, the patent inverts the approach by allowing users to draw arbitrary 2D curves on a reference surface and automatically generating the 3D surface to satisfy these curves as iso-parameter lines. This reverses the traditional workflow and greatly enhances modeling flexibility while maintaining control vertex sparsity
Solution Approach 2:
The patent changes the representation from fixed quadrilateral patches with constrained curve orientations to arbitrary-sided patches where the number of sides N can vary. This parameter change allows the patch topology to adapt to the user's artistic intent rather than forcing the art into rigid quadrilateral structures
3Ease of operation
If N-sided patches are used to alleviate constraints, then irregularities at vertices are reduced, but the initial polygon mesh control cage must still be developed which is challenging
Solution Approach 1:
The system performs self-service by automatically generating the N-sided patch control cage from the user's 2D curve sketches on the reference surface. The algorithm computes the 3D surface geometry and patch topology without requiring manual construction of the control cage, thereby maintaining ease of operation while handling vertex irregularities naturally through the N-sided patch structure
4Ease of operation
If sketch-based modeling tools are used for quick 3D shape modeling, then intuitive control is provided, but the ability to create sharp creases and complex surface features is limited
Solution Approach 1:
The patent introduces a sharpness parameter that controls the transition between smooth and sharp features at the boundary of the patch. By varying this parameter, the system can generate smooth continuous surfaces or surfaces with sharp creases along the sketched curves, greatly expanding the range of surface features while maintaining intuitive sketch-based control
Solution Approach 2:
The patent makes the surface characteristics dynamic by allowing the user to specify different smoothness levels at different locations along the boundary curve. The system dynamically adjusts the surface continuity (G0, G1, or higher) based on local constraints, enabling both smooth organic shapes and sharp geometric features within the same modeling framework
Data Source
AI summary
Methods and apparatus for generating an n-sided patch by sketching on a three-dimensional reference surface. A user draws a closed curve on a 3D surface; the drawn outline is taken as a boundary for an N-sided patch. If the user does not close the curve, the system may automatically close the curve, as a closed outer boundary curve may be required to produce an N-sided patch. The boundary conditions, the positions, and the surface normals at the boundary are inferred automatically from the 3D surface that the user has drawn the curve on. In addition, boundary curves for the same patch may be drawn on different 3D shapes; multiple 3D shapes may be used as the template or canvas on which the user draws curves from which a patch is to be generated.