Ellipsoid Obstruction Visualization via Implicit Functions
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Solution Overview
Problem
Current techniques for visualizing the region of obstruction in 3D spaces, particularly by ellipsoidal shapes, are inefficient in dynamic environments and struggle to accurately depict the field of view restrictions caused by such objects during animation and sensor operations.
Innovation Solution
The method employs Boolean operations on primitive elements represented as implicit functions and parametric surfaces to define and visualize the obstructed region, using ray-surface intersection solutions to render the boundary surface of the obstruction, effectively transforming the ellipsoidal problem into a unit sphere for simplified calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional rendering techniques are used to determine graphical elements in 3D scenes, then visualization accuracy is maintained, but computational efficiency deteriorates significantly during animation and dynamic scene rendering
Solution Approach 1:
The obstructed region is segmented into multiple primitive elements (cones, cylinders, and planes) that can be independently defined and rendered. This segmentation allows the complex obstruction problem to be broken down into simpler geometric components that can be efficiently processed during animation frames.
Solution Approach 2:
The patent transforms the 3D ellipsoidal obstruction problem into a 2D representation by defining the obstructed region using implicit functions and parametric surfaces. This dimensional transformation simplifies the computational complexity while maintaining visualization accuracy, enabling efficient rendering during dynamic animation sequences.
2Measurement precision
If the obstruction region is defined using complex geometric models, then visualization accuracy is improved, but device complexity and computational requirements increase
Solution Approach 1:
The patent uses implicit functions and parametric surfaces to define the boundary of the obstructed region, which naturally accommodate curved geometries. This approach maintains accurate representation of the ellipsoidal obstruction while avoiding the need for complex polyhedral models, thus balancing accuracy with computational efficiency.
3Manufacturing precision
If ray-surface intersection solutions are implemented for every frame, then obstruction boundary visualization is accurate, but computational time increases
Solution Approach 1:
The obstructed region is pre-defined using implicit functions and parametric surfaces before animation begins. This preliminary definition allows the system to quickly determine which graphical elements contribute to the scene during animation without performing complex ray-surface intersection calculations for every frame, significantly reducing processing time while maintaining boundary accuracy.
Data Source
AI summary
Methods, systems, and devices for the visualization of the region of a 3-dimensional space obstructed from a viewing location by an ellipsoid are disclosed. In an embodiment, the obstructed region may be defined from primitive elements which are combined using Boolean operations. The primitive elements chosen may be represented using both implicit functions and/or parametric surfaces. In an embodiment, the implicit function representation may be used to quickly determine points on candidate surfaces which may be obstructed from view. In an embodiment, the parametric representation may be used to provide ray-surface intersection solutions enabling visualization of the boundary surface of the obstruction region.