Transform-Aware Object Blending for Nested Geometric Repeats
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Solution Overview
Problem
Conventional systems struggle with accurately performing blending operations on complex objects formed using repeat transforms, often resulting in erroneous replications, loss of fidelity, and inability to handle nested repeat transforms, especially when the number of transforms increases.
Innovation Solution
The system identifies a primary object and transform sequence for each complex object, inverts the sequence to extract the primary object, and performs linear interpolation between these objects and their sequences to generate intermediate objects that preserve the fidelity of the geometric repeats.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional blending operations are applied to complex objects with repeat transforms, then blending can be performed, but the result suffers from erroneous replications and loss of fidelity
Solution Approach 1:
The patent segments the complex object into a primary object and a separate transform sequence. By identifying and extracting the primary object (the source geometry) and its associated repeat transform sequence, the system can manipulate the primary object independently while preserving the transform sequence intact. This segmentation allows blending operations to be applied correctly to the primary object without corrupting the repeat transform structure, thereby maintaining fidelity and avoiding erroneous replications.
Solution Approach 2:
The patent extracts the primary object from the complex object by inverting the repeat transform sequence. This extraction separates the geometric source (primary object) from the transformation instructions (repeat sequence), enabling independent processing. The primary object can be blended with another primary object while the repeat transform sequences are preserved and re-applied to the blended result, preventing loss of fidelity in the repeat transforms.
2Adaptability or versatility
If the number of repeat transforms increases to create more complex designs, then design complexity and creativity increase, but the system's ability to maintain fidelity during blending decreases
Solution Approach 1:
The patent segments complex objects with multiple nested repeat transforms into discrete primary objects and transform sequences. Each complex object is decomposed into its fundamental primary geometry and its associated transform instructions, regardless of how many repeat transforms are nested. This segmentation enables the system to handle high design complexity by processing each primary object independently through blending operations while preserving all transform sequences, thereby maintaining fidelity even as design complexity increases.
Solution Approach 2:
The patent performs preliminary identification and extraction of primary objects and their transform sequences before blending operations occur. By pre-processing the complex objects to separate primary geometries from transform instructions, the system prepares the data structure in advance to handle multiple nested transforms efficiently. This preliminary action ensures that when blending occurs, the fidelity of all repeat transforms is maintained regardless of their complexity or nesting depth.
3Productivity
If conventional blending is applied to complex objects, then blending operation can be executed, but intermediate shapes become distorted
Solution Approach 1:
The patent segments the blending operation into two distinct phases: (1) blending of primary objects to generate intermediate primary objects, and (2) application of intermediate transform sequences to generate final intermediate complex objects. By segmenting the operation this way, the system maintains accurate shapes throughout the blending process because the transform sequences are preserved and re-applied correctly at each intermediate step, preventing distortion while maintaining productivity.
Solution Approach 2:
The patent introduces intermediate primary objects as mediators in the blending process. These intermediate primary objects serve as the basis for generating intermediate complex objects by applying intermediate transform sequences. This intermediary approach ensures that each intermediate step maintains shape accuracy because the primary object geometry is properly blended while the transform sequences are correctly interpolated and applied, preventing distortion in the intermediate shapes.
Data Source
AI summary
Embodiments are disclosed for blending complex objects. The method may include identifying a first complex object and a second complex object. A first primary object associated with the first complex object and a first sequence of geometric repeat operations are determined. A second primary object associated with the second complex object and second sequence of geometric repeat operations are also determined. A blending operation is applied to the first primary object and the second primary object to generate one or more intermediate primary objects. One or more intermediate complex objects are generated from the one or more intermediate primary objects.