3D Model Deformation Using Smooth Mapping Functions
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Solution Overview
Problem
Current 3D CAD systems lack intuitive methods for deforming complex models while preserving smoothness, often requiring complex operations that are computationally costly and limiting user interaction to specific control points or curves, which restricts the ability to create desired shapes efficiently.
Innovation Solution
A computer-implemented method that uses smooth three-dimensional mapping functions to deform 3D models, allowing arbitrary lower-order geometry as deformation controls, such as points, curves, or surfaces, to directly manipulate models interactively, preserving smoothness and surface curvature through a sequence of smooth space mappings.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a finer control mesh is used to produce small features, then the ability to control surface modifications is improved, but memory requirements and computational cost increase
Solution Approach 1:
The patent segments the deformation process into a hierarchical structure: a coarse control mesh defines overall surface deformation, while local refinement techniques apply higher precision only to specific regions requiring small features. This allows the system to maintain fine control where needed without globally increasing mesh complexity.
Solution Approach 2:
The patent implements local quality by allowing different regions of the surface to have different levels of control mesh refinement. Areas requiring high precision for small features use finer local meshes, while other regions use coarser meshes, optimizing the balance between control precision and computational resources.
2Ease of operation
If space deformation is applied to vertices of a mesh, then deformation operation is simplified, but sharp edges may be exaggerated and polygon aspect ratios deteriorate
Solution Approach 1:
The patent changes the deformation parameters by applying transformations to polygons and surfaces rather than just vertices. This involves modifying face normals, polygon positions, and surface definitions in a coordinated manner to maintain geometric integrity while achieving the desired deformation effect.
Solution Approach 2:
The patent introduces intermediary computational steps between vertex deformation and final rendering. These intermediaries include recalculating face normals, adjusting polygon positions, and applying corrective transformations to preserve sharp edges and proper aspect ratios after the primary deformation is applied.
3Shape
If the degree of smoothness of subdivision surface is increased, then surface quality is improved, but computational cost and memory requirements increase
Solution Approach 1:
The patent implements dynamic smoothness control where the degree of surface smoothness can be adjusted based on viewing distance, importance of the surface region, and computational resources available. This allows the system to maintain high smoothness for critical surfaces while using lower smoothness for less important areas, optimizing performance.
4Adaptability or versatility
If arbitrary point or curve is used as manipulation control, then user ability to form desired shape is improved, but resulting surfaces require high density control grids which are computationally expensive
Solution Approach 1:
The patent segments the control structure into a hierarchical system where a coarse control grid defines overall shape transformations, and local refinement algorithms generate finer control points only in regions affected by arbitrary point or curve manipulations. This maintains shape formation versatility while avoiding global high-density grid requirements.
Data Source
AI summary
Deforming a three-dimensional computer-generated model to cause a change of shape of the three-dimensional model includes representing a surface of the model using a surface representation initially comprised of an original surface definition, deriving smooth three-dimensional mapping functions where each mapping function defines a deformation to the surface and at least one mapping function is non-affine, constructing a composition of the mapping functions and the original surface definition where each mapping function is included in the composition in succession in accordance with the order of derivation, and applying the composition after each successive mapping function is included in the composition causing the surface of the three-dimensional model to be deformed while preserving the smoothness to the lowest degree of smoothness of the mapping functions.