Discussion Overview
The discussion revolves around the computation of the center of irregular convex hexahedras, specifically addressing the definition and calculation methods for determining the "center" of such shapes. Participants explore different interpretations of "center," including geometric and volume-based considerations, within the context of a 3-D structured mesh grid.
Discussion Character
- Exploratory
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant suggests that the center of a hexahedron can be computed as the sum of the indices divided by the number of indices, questioning if this holds true for all polygons and polyhedra.
- Another participant challenges the definition of "center" in irregular shapes, prompting a discussion on what is meant by "geometrical/spatial center."
- A participant expresses uncertainty about whether they are referring to a volume-based center, noting that averaging the vertices may not yield the center of volume.
- There is a mention of the center of mass having a clear definition, suggesting that the term "center" is too vague without further specification.
- One participant raises the concept of the centroid of a triangle and its relation to the centroid of a hexagon, indicating that the centroid can be calculated as a weighted average of the centroids of constituent triangles.
- A later post reiterates the initial question about the validity of averaging the indices to find the center, providing an example involving a cube transformed into a pyramid shape to illustrate the discrepancy between average coordinates and center of mass.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the definition of "center" or the appropriate method for calculating it in the context of irregular hexahedras. Multiple competing views regarding the interpretation and calculation methods remain present.
Contextual Notes
Participants express uncertainty regarding the assumptions behind the definitions of "center" and the implications of using different averaging methods. The discussion highlights the need for clarity in terminology and the potential limitations of various approaches.