Mesh Boundary Smoothing via Vertex Projection

The patent segments the mesh boundary into individual vertices and processes each vertex independently through incremental shifting. Instead of applying a global smoothing algorithm that affects the entire boundary uniformly, the method divides the boundary into discrete vertex elements that can be moved independently while maintaining their relationship to the initial surface, thereby preserving sharp edges and defined extrusion geometry.

The patent performs preliminary action by storing the initial surface geometry before any smoothing operations are applied. This initial surface serves as a reference that constrains subsequent vertex movements, ensuring that vertices are shifted only to positions that maintain the original mesh shape and definition. This preliminary preservation of geometric information prevents the rounding and loss of definition that occurs with conventional smoothing.

The patent implements self-service by creating an automated incremental vertex shifting algorithm that performs smoothing operations without requiring manual user intervention. The system automatically identifies boundary vertices, calculates their new positions based on the initial surface reference, and applies the shifts systematically. This automated process eliminates the tedious manual smoothing operations while maintaining high productivity through efficient computational processing.

The patent replaces the mechanical manual interaction (user manually moving vertices) with a computational algorithmic system. Instead of requiring users to repeatedly select and move vertices manually, the system uses automated calculations to determine optimal vertex positions and applies transformations computationally. This substitution of mechanical manual operations with automated computational processes dramatically improves productivity while achieving the same smoothing effect.

The patent introduces the initial surface geometry as an intermediary reference between the original vertex positions and the smoothed positions. This intermediary surface acts as a constraint that guides vertex movements, ensuring that vertices are shifted only along paths that maintain the original mesh shape. The initial surface serves as a mediating structure that allows boundary smoothing while preventing distortion of the overall mesh composition and surrounding regions.

The patent applies parameter changes by systematically adjusting vertex positions based on controlled incremental shifts rather than large arbitrary movements. The vertex displacement is managed through parameterized transformations that are constrained by the initial surface geometry, allowing gradual smoothing while maintaining mesh stability. This controlled parameter adjustment prevents the distortion that would result from uncontrolled vertex relocation.