Geometric Area Projection Determination for Multidimensional Objects
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Solution Overview
Problem
Current techniques are inefficient and inaccurate in determining the geometric area of projection (GAP) of multidimensional digital objects in computer-generated environments, which is crucial for visualization and rendering in various fields.
Innovation Solution
A system and method that includes modules for determining visible faces, vertices, and polygons of a multidimensional object, projecting these onto a viewport space, and calculating the geometric area of projection using normalized coordinates, enabling accurate estimation of the projected area relative to the viewport area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current techniques are used to determine the geometric area of projection, then the process can be completed, but the determination is inefficient and inaccurate
Solution Approach 1:
The patent segments the multidimensional object into discrete faces, vertices, and edges. By dividing the object into these geometric components, the system can systematically process each face to determine visibility and calculate projected area, thereby improving both accuracy and efficiency of the geometric area of projection determination
Solution Approach 2:
The patent transforms the three-dimensional geometric problem into a two-dimensional viewport space calculation. By projecting 3D faces onto a 2D viewport and using normalized device coordinates, the system efficiently calculates the geometric area of projection in the lower dimension, resolving the contradiction between measurement precision and productivity
2Measurement precision
If complex multidimensional objects are rendered, then visualization quality improves, but calculation complexity increases
Solution Approach 1:
The patent changes the parameter space by using normalized device coordinates (NDC) with a standardized coordinate system where the viewport is defined as a unit square. This parameter transformation simplifies the calculation of projected areas by eliminating the need for complex perspective divisions and coordinate transformations, thereby reducing calculation complexity while maintaining rendering precision
Solution Approach 2:
The patent creates a simplified 2D representation (copy) of the 3D object's visible faces in the viewport space. By working with these projected 2D polygons instead of the original complex 3D geometry, the system maintains visualization quality while significantly reducing the computational complexity of area calculations
Data Source
AI summary
Using various embodiments, systems, methods and techniques to determine whether a surface of the multidimensional object is projected on a camera on a viewport space displayed on a graphical user interface. This includes projecting a first vector normal to a surface of the multidimensional object, where the multidimensional object is rendered in an electronically generated multidimensional environment, projecting a second vector from the camera to the surface of the multidimensional object, determining an angle between the first vector and the second vector, and based on the angle determining whether the surface is projected on the viewport space.