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### Ill Check It - Side FX - Primitive Origin 1994 In Houdini and Mantra, Primitives all have an implicit parametric space, sometimes called primitive UVs, for referring to positions on their surfaces, or other interpolations of Geometry attributes on their points or vertices.

These coordinates can then be used for interpolation within primitives, for example, if they're deforming over time, by the Attribute Interpolate node or the primuv VEX functions. Quadrics: Spheres, Tubes, Circles.

Triangle parametric spaces in Houdini have vertex 0 at the origin, 0,0vertex 1 at the u axis unit, 1,0and vertex 2 at the v axis unit, 0,1. The barycentric coordinate associated with vertex 0 is 1-u-v. These give the 3 linear interpolation weights for the 3 vertices, e.

Half of the uv unit square is unoccupied, though some cases may mirror the other half onto the first half if provided coordinates out of range. Quads are treated as bilinear patches in Houdini, Ill Check It - Side FX - Primitive Origin smoothly, consistently handle cases where the 4 vertices are Tomato Kisser - Shorty - Fresh Breath EP all in the same plane non-planarat the expense of that quads are quadratic surfaces, instead of flat surfaces like triangles.

Quad parametric spaces also have vertex 0 at the origin, however, vertex 1 is instead at the v axis unit, 0,1and vertex 3 is at the u axis unit, 1,0 ; vertex 2 is at 1,1. Note that non-convex quads will usually still be treated as bilinear patches, which will self-overlap in these cases. This is sometimes unwanted, so if you need non-convex quads to be triangulated, you can use the Divide Ramses Bringer Of War - Nile - In The Beginning node with Convex Polygons enabled, and Maximum Edges set as needed, e.

Bowtie quads are more difficult to split well if the bilinear interpretation is not acceptable, but can be fixed with a combination of options on the Triangulate 2D. For triangles in Mantra, the implicit uv coordinates of a triangle will be those of a quad bilinear patch with vertex 0 duplicated. The triangles and quads in the diagram all have normals pointing into the screen, so these are showing the back faces.

The normal direction is "left-handed" relative to the winding order. Many other 3D geometry programs use "right-handed" normals, so you may need to use a Reverse node to reverse the winding order of polygons when importing from another software package.

Polygons with 5 or more sides are often referred to as "n-gons", to distinguish that they need to be handled differently from triangles or quads.

In order to have at least one implicit uvw coordinate corresponding with each point in a non-convex n-gon, Houdini implicitly covers the space with a triangle fan around the average of all of the vertices.

The boundary parameterization is Ill Check It - Side FX - Primitive Origin to that of a polygon curve if it had an extra vertex wrapping Ill Check It - Side FX - Primitive Origin back around to vertex 0. However, because there are polygons that are not " star-shaped " or that do not have the center in their kernels, there can be both points outside the polygon that have parametric coordinates in the unit square, and points inside the polygon that have multiple parametric coordinates, possibly even multiple positions if the polygon Youre My Heart - LL Cool J - Walking With A Panther non-planar.

A single implicit uvw coordinate still always represents a single position. It does, however, mean that for polygons with many sides, the time required to determine the coordinate or interpolate the polygon from one takes time proportional to the number of sides, so can be slow for polygons with hundreds or thousands of sides.

Mantra always splits polygons with 5 or more sides into triangles and quads, with a similar method to the one used by the Divide geometry node with Maximum Edges set to 4. This avoids some issues of the coordinate system used in Houdini, but at the expense of multiple positions having the same parametric coordinate and instability.

This will avoid any popping in the renders that would have come from the n-gon splitting changing. The n-gon in the diagram has normals pointing into the screen, so this is showing the back face.

The normal direction is "left-handed" relative to the winding order, just as with triangles and quads. Polygons in Houdini can also have what are known as "bridges", which are edges a polygon shares with itself, to be able to construct "holes". There are many ways to create bridges to holes, especially if there are multiple holes, since a hole can bridge to another hole, as shown in the diagram. The one primary requirement of bridges is that they are not allowed to cross an edge of the polygon, including other bridge edges and edges of the holes.

Curves also have width in Mantra, and u goes from 0 to 1 along the width of the curve. Closed polygons with 0, 1, or 2 vertices are degenerate, and open polygons polygon curves with 0 or 1 vertices are degenerate.

The parametric space of a polygon with zero vertices is ill-defined. The Emmanuelle - Javier Elorrieta - Aranjuez Mon Amour space of a polygon with 1 vertex should have that vertex fill the entire space, or put in the reverse sense, all parametric coordinates map onto that vertex. A closed polygon with 1 vertex Ill Check It - Side FX - Primitive Origin sometimes treated as having 1 edge from its vertex back to itself, to maintain that the number of edges is equal to the number of vertices, though other times it is treated as having no edges.

A closed polygon with 2 vertices is sometimes treated as a polygon curve with 2 vertices, though it is sometimes treated as having two of the same edge. Polygon soups represent multiple faces in a single primitive.

Each face has implicit u and v coordinates equivalent to the corresponding coordinates of an equivalent closed polygon primitive. The w coordinate is used to indicate which face in the soup is referenced.

If the face number within the soup is 16, i. For faces beyond that up to 1. Tetrahedra tets in Houdini are sometimes considered solid, e. This is useful for determining the parametric coordinates of points of a point cloud embedded in a tetrahedral mesh. However, sometimes only the unshared faces, the surface of a tetrahedral mesh, are considered, e.

The boundary of the tetrahedral mesh, transition into or out of it, is more likely to be the desired result in these cases. In both situations, the paramteric uvw coordinates are reported the same way. Similar to triangles, vertex 0 is at the origin, 0,0,0vertex 1 at the u axis unit, 1,0,0vertex 2 at the v axis unit, 0,1,0and vertex 3 at the w axis unit, 0,0,1. Also similar to triangles, u, v, and w are equivalent to the barycentric coordinates associated with vertex 1, vertex 2, and vertex 3.

The barycentric coordinate associated with vertex 0 is 1-u-v-w. These give the 4 linear interpolation weights for the 4 vertices, e. The triangular faces in the diagram all have normals pointing into the screen, so these are showing the back faces. The normal direction is "left-handed" relative to the winding order, as with polygon primitives. Tetrahedra have the additional consideration that they can be inverted, i. Note that if you assign the implicit uvw Ill Check It - Side FX - Primitive Origin corresponding with each vertex to the point positions, the tetrahedron will be inverted.

All tetrahedra are assumed to have 4 vertices. If one is constructed in the HDK with a different number of vertices, code may crash or produce nonsensical results. The addprim and addvertex VEX functions will not Ill Check It - Side FX - Primitive Origin construction of one with a different number of vertices.

Volumes only have one vertex, so there is only interpolation of P and voxel values. A single volume primitive in Houdini only represents a single bit floating-point value in each voxel. Multiple volume primitives can be logically grouped into an effective vector volume using a name primitive string attribute, using names like "Cd. Volumes that have only one voxel in one of the parametric directions, 2D volumes, can be treated as flat images in various places in Houdini.

The inverse is done in the reverse order to compute parametric coordinates for a position. For 2D heightfield volumes, the value of the volume evaluated at the parametric coordinates for the axes that have more than 1 voxel in them, is used as the displacement from the center plane along that axis.

Voxel data in volume primitives are treated as cell-centered. Between voxel centers, data are interpolated trilinearly. The 0 and 1 parametric values correspond with the beginning of the first voxel and the end of the last voxel in some parametric axis, respectively. These coordinates are not between voxel centers, though, being on the boundary, so are handled like out-of-bounds values, using either the "constant", "repeat", "streak", or "sdf" border type, which can be seen in the volumebordertype primitive intrinsic.

The voxel data are intended to be signed distances to the implicit surface. A tile that contains only a constant value for all of its voxels can be represented by that single value, instead of a full grid of its data. This allows more efficient representation of sparse volume data. VDBs are an open standard volume representation optimized for very sparse volume data, usually only having bottom-level voxel data in a "narrow band", using a 4-level tree of tiles that can be constant at any level.

The top level can be an arbitrary resolution, but the other levels are a fixed power-of-two resolution in each tile, down to voxels at the bottom. Unlike most other primitive types, the parametric space of a VDB is not limited to the range 0,0,0 to 1,1,1.

The space is identical to the bottom level voxel index space, Quicksand - Clark Terry - Yes, The Blues voxel indices can be negative, depending on the shift of the top level grid. This allows adding of new voxel data anywhere up to roundoff error considerationswithout changing the parametric coordinates of existing data.

The transform of the VDB grid, including any frustum transformtransforms directly from voxel index space to physical space. However, often only the narrow band has correct signed distances to the implied surface, whereas the constant tile data values outside of the narrow band may only have the correct sign, not an actual distance.

Some VDBs instead represent "fog volumes", where the values represent densities or other values. Outside of the range of occupied tiles, there is a "background value" of any given VDB. Like volume primitives, VDBs only have Ill Check It - Side FX - Primitive Origin vertex, so Photograph - Carousel - 2113 is only interpolation of P and voxel values.

Working with objects. Points and vertices. Geometry attributes. Describes how Houdini represents geometry using details, primitives, points, vertices, and attributes.

Create geometry. Edit geometry. Edit components. Reselect geometry. In Houdini you can not only edit the parameters of a surface node, you can reselect the geometry the operation applies to.

Polygon shelf tools. Model shelf tools. Mirror geometry across a symmetry plane. Repair polygonal models. Snapping, construction plane, and alignment. Building terrain with height fields. Realistic terrain with heightfields. A heuristic workflow using the heightfield tools, based on experience generating realistic-looking terrain. See Destruction. Import geometry from other objects.

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### 8 thoughts on “ Ill Check It - Side FX - Primitive Origin ”

##### Tem Oct 2, 2012 at 10:12 pm Reply
The parametric space of a polygon with zero vertices is ill-defined. The parametric space of a polygon with 1 vertex should have that vertex fill the entire space, or put in the reverse sense, all parametric coordinates map onto that vertex.