5 Vertex

[Luciana]

Ingeometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.[1][2][3]

The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments, and lines that result in two straight "sides" meeting at one place.[3][4]

Polytope vertices are related to vertices of graphs, in that the 1-skeleton of a polytope is a graph, the vertices of which correspond to the vertices of the polytope,[6] and in that a graph can be viewed as a 1-dimensional simplicial complex the vertices of which are the graph's vertices.

However, in graph theory, vertices may have fewer than two incident edges, which is usually not allowed for geometric vertices. There is also a connection between geometric vertices and the vertices of a curve, its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve, there will be a point of extreme curvature near each polygon vertex.[7]

A vertex of a plane tiling or tessellation is a point where three or more tiles meet;[8] generally, but not always, the tiles of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles. More generally, a tessellation can be viewed as a kind of topological cell complex, as can the faces of a polyhedron or polytope; the vertices of other kinds of complexes such as simplicial complexes are its zero-dimensional faces.

where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.

In computer graphics, objects are often represented as triangulated polyhedra in which the object vertices are associated not only with three spatial coordinates but also with other graphical information necessary to render the object correctly, such as colors, reflectance properties, textures, and surface normal.[11] These properties are used in rendering by a vertex shader, part of the vertex pipeline.

I'm doing a project in ArcGIS Pro where polygons are incredibly important to separate data from one another. We run a tool that draws the polygons themselves, and then finds errors where overlaps happened. Part of what I'm doing is cleaning up those overlaps to run the tool again until its clean. In order to fix them, I just have to grab the polygon, edit vertices and reroute a few things where they arent touching.

Easy, right? Well it was. I'm not sure what happened, but now every time I edit vertices on a polygon and let it process, it moves the entire polygon a good bit. In doing so it excludes data that needs to be in there by bumping it out of the polygon, and causes more overlaps. I didnt catch it at first because it wasnt doing it for a few days. But when i made fixes, it created a whole slew of other issues. I'm now seeing it, and have to snap to a reference point, and use the move tool to move the entire polygon back to its original position. This obviously is not ideal.

Any ideas on what would be causing the polygon to move? When editing vertices im VERY careful that i'm only grabbing the vertex to move, as in im not grabbing the polygon line and moving it. This has gotten really frustrating!

I just toggled both on, both off, and one and not the other and none of them help with what's going on. Its not when I'm moving the vertex, its after I move it to where i want it, when the change happens it moves exactly how i want it, then the entire polygon remains intact but shifts several feet (in this scale its a small amount, but these are tight polygons and have to be).

I have a mesh which has per-vertex colours. I seem unable to quickly turn off these colours in Rhino. Is this possible or is there a specific workflow that I have to follow to see my mesh without any colours?

Cheers!

since ive been unsure how many vertex colors can be stored in a user string, ive changed the code to use a user dictionary as Willem suggested. (Thanks by the way for mentioning it, it seems much more comfortable).

Im still storing the vertex colors as integer values using a System.Array. As far as i understand the maximum amount of vertex color integers the Array can store under 32bit equals 4.294.967.295 colors. (See Remarks section here) I hope this is enough

this thread is about how to disable and later re-enable mesh vertex colors which could be done with a script or by adjusting the display mode properties. To get rid of mesh vertex colors, you might use the _RebuildMesh command without having the mesh preselected. Then set the command options like below:

The Vertex Shader is the programmable Shader stage in the rendering pipeline that handles the processing of individual vertices. Vertex shaders are fed Vertex Attribute data, as specified from a vertex array object by a drawing command. A vertex shader receives a single vertex from the vertex stream and generates a single vertex to the output vertex stream. There must be a 1:1 mapping from input vertices to output vertices.

Vertex shaders typically perform transformations to post-projection space, for consumption by the Vertex Post-Processing stage. They can also be used to do per-vertex lighting, or to perform setup work for later shader stages.

The OpenGL specification is fairly lenient on the number of times a vertex shader is invoked by the rendering system. Vertex Specification and Vertex Rendering define a vertex stream: an ordered sequence of vertices to be consumed. The vertex shader will be executed roughly once for every vertex in the stream.

A vertex shader is (usually) invariant with its input. That is, within a single Drawing Command, two vertex shader invocations that get the exact same input attributes will return binary identical results. Because of this, if OpenGL can detect that a vertex shader invocation is being given the same inputs as a previous invocation, it is allowed to reuse the results of the previous invocation, instead of wasting valuable time executing something that it already knows the answer to.

OpenGL implementations generally do not do this by actually comparing the input values (that would take far too long). Instead, this optimization typically only happens when using indexed rendering functions. If a particular index is specified more than once (within the same Instanced Rendering), then this vertex is guaranteed to result in the exact same input data.

Therefore, implementations employ a cache on the results of vertex shaders. If an index/instance pair comes up again, and the result is still in the cache, then the vertex shader is not executed again. Thus, there can be fewer vertex shader invocations than there are vertices specified.

Each user-defined input variable is assigned one or more vertex attribute indices. These can be explicitly assigned in one of three ways. The methods for assigning these are listed in priority order, with the highest priority first. The higher priority methods take precedence over the later ones.

Note that like uniforms, vertex attributes can be "active" and non-active. Active inputs are those that the compiler/linker detects are actually in use. The vertex shader and GLSL program linking process can decide that some input are not in use and therefore they are not active. This is done even if an explicit attribute index is assigned in the vertex shader.

Attributes may be arrays, matrices, and double-precision types (if OpenGL 4.1 or ARB_vertex_attrib_64bit is available). Or combinations of any of these. Some of these types are large enough to require that the input variable be assigned to multiple attribute indices.

These combine with each other. A mat2x4[2] array is broken up into four vec4 values, each of which is assigned an index. Thus, it takes up 4 indices; the first two indices specify the two columns of array index 0, and the next two indices specify the two columns of array index 1.

Even though there are 4 total attribute indices available after the a_matrix* indices are assigned, they cannot be assigned sequentially. There is no attribute index for bad_matrix that will allow it to get 4 sequential indices. Thus, the linker will fail.

There is a case which makes this more complex: double-precision attributes (if OpenGL 4.1 or ARB_vertex_attrib_64bit is available). dvec3 and dvec4 only take up one attribute index. But implementations are allowed to count them twice when determining the limits on the number of attributes. Thus, while a dmat2x3[4] will only take up 8 attribute indices (4 array elements of 2 columns of dvec3s), the implementation is allowed to consider this as taking up 16 indices when determining if a shader is using up too many attribute indices. As such, a dmat2x3[5] may fail to link even though it only uses 10 attribute indices.

Note the use of the word "allowed". The implementation is free to count them only once, but you can't rely on it. So you need to assume that these will consume two input resources, even though they only use one index. Since there is no way to query whether any particular implementation will count them twice, you must assume that they will take up two resources.

Output variables from the vertex shader are passed to the next section of the pipeline. Many of the next stages are optional, so if they are not present, then the outputs are passed to the next one that is. They are in this order:

User-defined output variables can have interpolation qualifiers (though these only matter if the output is being passed directly to the Vertex Post-Processing stage). Vertex shader outputs can also be aggregated into Interface Blocks.

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