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  • integration - Is there formula for the volume of a hexahedron . . .
    Is there formula for the volume of a hexahedron? Ask Question Asked 11 years, 1 month ago Modified 8 years, 8 months ago
  • Mapping a 3D point inside a hexahedron to a unit cube
    Let A4x8 be a hexahedron defined by 8 points in 3D homogeneous coordinates M8x8 is a map that transforms the hexahedron to a unit cube, B4x8 If A = B M, then M = B-1 A How can I map a 3D
  • solution verification - If seven vertices of a hexahedron lie on a . . .
    What does hexahedron mean in this case? Not all hexahedra have eight vertices I must be missing something: Given some polyhedron with vertices on a sphere, nothing stops me from moving just one vertex a little bit "outwards" (in radial direction away from the center of the sphere) to get another polyhedron with the same number of faces, edges and vertices, but with one corner outside the ball
  • Map an xyz coordinate inside a hexahedron to normalized 0-1 space
    How do I map this new coordinate into the hexahedron's space where 0-1 defines the space inside the hexahedron in each axis? Research I have done leads me to think the answer lies in matrix math "change of basis" operations
  • Calculate the surface area of each face of a hexahedron and its . . .
    Hi, since this can be an arbitrary hexahedron in a finite element mesh I wanted to use an isoparametric transformation formula It would not be feasible to calculate using the physical coordinates for all the elements I know that the area can be found using cross product of the two sides but wanted to know if there is any room for exploration using the isoparametric formulation
  • Simple general formula for the volume of a 8-vertices hexahedron
    I know that the hexahedron can be subdivided in 5 tetrahedra, and we can compute the volume for each tetrahedron using a simple matrix determinant More precisely, let us number the vertices from 1 to 8, one face being 1234, its opposite face 5678 (with the same orientation), and vertices 1 and 5 being on the same segment
  • Hexahedron congruent faces - Mathematics Stack Exchange
    Hexahedron congruent faces Ask Question Asked 9 years ago Modified 3 years, 10 months ago
  • Hexahedron made with similar polygons - Mathematics Stack Exchange
    A similar 2D hexahedron can be made with a piece of my rho-quad tiling, where ρ ρ = plastic constant One goal is to find a polyhedron that sorta splits into 2 or more similar polyhedra where most of the vertices align, much like what is being done with polygons in the psi-quad and rho-quad tilings But for this post, a simpler question:
  • How to determine the orientation of convex concave hexahedra?
    However, the issue I have is that there are certain geometric operations (e g reflection about a plane) in my code that flip the orientation of a given hexahedron I am currently able to check the orientation robustly for convex hexes by computing the centroid and ensuring that the face normals are outward-pointing with respect to it
  • How to determine the outward normal vector of a face of a hexahedron if . . .
    Your hexahedron is convex, so you can do the dot product of the normal vector that you found, and a vector from one of the vertices to some point inside the hexahedron If the dot product is negative, then your normal vector points out If you already know a point inside the hexahedron, then you're in luck Otherwise you would have to find this, which would pose challenges of its own





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