Blending Arbitrary Pipe Surfaces via Spherical Parametrization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional CAD modeling subsystems are unable to effectively blend arbitrary pipe surfaces, such as cylinders and cones, due to limitations in existing blending algorithms that fail to produce sufficiently smooth surfaces and satisfy high curvature continuity constraints, making it difficult to meet functionality, aesthetic, and manufacturing requirements.
Innovation Solution
A computer-implemented method using spherical parametrization to trim and blend surfaces by projecting trimming curves onto a fundamental sphere and then mapping them to a two-dimensional parametric domain, generating a parametric blending surface that satisfies G2 continuity constraints, allowing for the creation of smooth intersections between arbitrary pipe surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional blending algorithms are used in CAD modeling subsystems, then the algorithms are compatible with parametric surfaces, but the algorithms are unable to effectively blend arbitrary pipe surfaces such as cylinders and cones
Solution Approach 1:
The patent introduces an implicit blending algorithm as an intermediary component that operates outside the traditional parametric surface framework. This implicit algorithm serves as a mediator that can handle arbitrary pipe surfaces (cylinders, cones) by defining blending surfaces through implicit equations rather than parametric representations, thereby extending CAD capabilities to previously unsupported geometries while maintaining G2 continuity
Solution Approach 2:
The patent fundamentally changes the mathematical representation parameters from parametric surfaces (u,v) to implicit surfaces F(x,y,z)=0. This parameter transformation enables the blending algorithm to operate on arbitrary pipe surfaces by using level sets and implicit equations, which can naturally represent complex geometries like cylinders and cones while ensuring high curvature continuity through the implicit formulation
2Adaptability or versatility
If implicit blending algorithms are used to operate on a wide range of surfaces, then the algorithms can blend arbitrary surfaces, but the algorithms generate implicit surfaces in Euclidean space 3 which are incompatible with CAD modeling subsystems that operate on parametric surfaces
Solution Approach 1:
The patent segments the blending process into distinct phases: implicit surface generation for the blending region, intersection computation with existing parametric surfaces, and extraction of parametric representations for the final model. This segmentation allows the implicit algorithm to handle arbitrary surfaces while the output is converted to parametric form compatible with CAD subsystems
Solution Approach 2:
The patent transitions from the traditional 2D parametric domain (u,v) to 3D implicit space F(x,y,z)=0, adding a dimensional perspective that enables handling of arbitrary surfaces. By working in the implicit 3D space and then projecting back to parametric representations, the system gains the versatility of implicit methods while maintaining CAD compatibility
3Manufacturing precision
If parametric blending surfaces are generated to join trimmed surfaces, then the blending surface can be integrated into the model, but the existing algorithms do not produce sufficiently smooth surfaces to meet G2 or higher continuity constraints
Solution Approach 1:
The patent performs preliminary trimming of surfaces along blending curves before generating the blending surface. By pre-defining the trimmed boundaries and using these as constraints for the implicit blending algorithm, the system ensures that the resulting blending surface automatically satisfies G2 continuity requirements while simplifying the overall manufacturing process
Data Source
AI summary
In various embodiments of the present invention, a blending engine blends multiple surfaces included in a three-dimensional (3D) model of an object. First, the blending engine trims off portions of the surfaces that are targeted for blending at trimming curves to generate trimmed surfaces. The blending engine then constructs a single parametric blending surface via a unified parametrization for the trimming curves. Notably, to achieve the unified parametrization, the blending engine performs one or more spherical parametrization operations that generate parametrized curves based on the trimming curves and a fundamental sphere. After constructing the parametric blending surface based on the parametrized curves, the blending engine joins the parametric blending surface to the trimmed surfaces to produce a final, smooth intersection between the surfaces. Advantageously, because the blending engine creates a single parametric blending surface, the blending engine can blend arbitrary pipe surfaces and is compatible with computer-aided design modeling subsystems.