3D Object Representation Using Signed Distance Functions
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing techniques for representing three-dimensional objects in graphics and imaging require large storage and computational efforts, as they often rely on coordinate-based representations or complex hierarchical schemes, which are inefficient and cumbersome.
Innovation Solution
The method involves constructing a bounding box with a bounding plane in a 3-D coordinate system, projecting a ray from a grid point to the object, and computing a parameterization value based on the distance from the grid point to the intersection point, using signed distance functions for efficient representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If coordinate-based representation is used for 3-D objects, then the object data can be represented with respect to a coordinate system, but the storage requirements and computational efforts increase significantly
Solution Approach 1:
The patent extracts only the essential geometric information needed for object representation by using signed distance functions that encode distance and orientation data. Instead of storing complete coordinate information for all points, the method extracts and stores only the minimal necessary parameters (distance values and normal vectors) to reconstruct the object surface, significantly reducing storage requirements while maintaining representation accuracy.
Solution Approach 2:
The patent transforms the representation from storing raw coordinate data to storing derived parameters (signed distance values and surface normals). This parameter transformation allows the object to be represented more efficiently by encoding geometric properties directly rather than storing positional data for numerous points, reducing the quantity of data needed while preserving measurement precision.
2Productivity
If hierarchical representation schemes like octree are used, then the object can be represented at several levels of hierarchy, but complex data structures and computation efforts are required to traverse the trees
Solution Approach 1:
The patent replaces the mechanical tree-traversal system with a direct mathematical field representation. Instead of navigating hierarchical data structures through complex traversal algorithms, the method uses continuous signed distance functions that can be evaluated directly at any point in space. This substitution eliminates the need for complex data structure manipulation while maintaining the ability to represent objects at multiple levels of detail through field sampling.
Solution Approach 2:
The patent transitions from discrete hierarchical levels to a continuous mathematical field representation. By using signed distance functions defined over continuous space rather than discrete hierarchical tiers, the method eliminates the need to traverse between levels. The continuous field approach allows direct access to geometric information at any resolution level without the structural complexity of hierarchical navigation.
3Reliability
If complete object data is stored in memory, then the representation is complete and accurate, but the memory consumption increases
Solution Approach 1:
The patent uses implicit representation where the complete object geometry is not stored explicitly but is instead copied on-demand through evaluation of the signed distance function. The function itself serves as a compact generator that can produce complete and accurate object data when needed, without requiring the full dataset to be stored in memory. This allows memory consumption to be dramatically reduced while maintaining representation completeness through functional evaluation.
Data Source
AI summary
An embodiment of the present invention includes a technique to represent three-dimensional (3-D) object using signed distance functions. A bounding box containing an object is constructed in a 3-D coordinate system. The bounding box has at least a bounding plane. A ray is projected from a grid point on the bounding plane to the object with a pre-defined direction. The ray intersects a surface of the object at an intersection point. A parameterization value of the intersection point associated with the grid point is computed. The parameterization value corresponds to a distance from the grid point to the intersection point.