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Directional vector associated with a vertex
a vertex normal at a vertex of a polyhedron is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of
Vertex_normal
Geometry definition file format
alone – namely, the position of each vertex, the UV position of each texture coordinate vertex, vertex normals, and the faces that make each polygon
Wavefront_.obj_file
Line or vector perpendicular to a curve or a surface
components – Mathematical vector components Vertex normal – Directional vector associated with a vertex Mean curvature – Differential geometry measure
Normal_(geometry)
Set of polygons to define the surface of a 3D model
used by a vertex shader or vertex pipeline. Attributes can include position, color, reflectance, specularity, texture mapping coordinates, normal vectors
Polygon_mesh
Point where two or more curves, lines, or edges meet
and surface normal. These properties are used in rendering by a vertex shader, part of the vertex pipeline. Vertex arrangement Vertex figure Weisstein
Vertex_(geometry)
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Shading language
transforming the vertex from object space to view space, generating texture coordinates, and calculating lighting coefficients such as the vertex's normal, tangent
High-Level_Shader_Language
Low-level shading language
a frame buffer for display. Attrib parameters are per-vertex attributes such as vertex normals. Local parameters are applied across a program's entire
ARB_assembly_language
Depicting depth with levels of darkness
Determine the normal at each polygon vertex. Apply an illumination model to each vertex to calculate the light intensity from the vertex normal. Interpolate
Shading
Interpolation technique for surface shading
shading, a normal vector is linearly interpolated across the surface of the polygon from the polygon's vertex normals. The surface normal is interpolated
Phong_shading
Type of program in computer graphics
shaders. The first shader-capable GPUs only supported pixel shading, but vertex shaders were quickly introduced once developers realized the power of shaders
Shader
2020 video game
slopes was made possible through boosting the overlay texture when the vertex normal looked up; however, this presented complications in ground features
Cyberpunk_2077
3D computer graphics software
(Calculate Simulations via CPU or GPU) Pyro (New Emission Type - Points) Vertex Normal Editing (New Editing Manager) Modeling (New Options and Improvements)
Cinema_4D
Feature of OpenGL for storing vertex data
A vertex buffer object (VBO) is an OpenGL feature that provides methods for uploading vertex data (position, normal vector, color, etc.) to the video
Vertex_buffer_object
The curved point-normal triangle, in short PN triangle, is an interpolation algorithm to retrieve a cubic Bézier triangle from the vertex coordinates of
Point-normal_triangle
On bipartite matching and vertex cover
A vertex cover in a graph is a set of vertices that includes at least one endpoint of every edge, and a vertex cover is minimum if no other vertex cover
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Medical condition
Normal pressure hydrocephalus (NPH), also called malresorptive hydrocephalus, is a form of communicating hydrocephalus in which excess cerebrospinal fluid
Normal_pressure_hydrocephalus
File format used by the Autodesk 3ds Max
number of vertices and polygons per mesh is limited to 65536. Accurate vertex normals cannot be stored in the .3ds file. Instead "smoothing groups" are used
.3ds
and caching the results in a texture map or vertex attributes. Typically used for generating lightmaps, normal maps, or low level of detail models. Barycentric
Glossary_of_computer_graphics
Simulation of light in computer graphics
polygon are a blend of its vertex values. Each vertex is given its own normal consisting of the average of the surface normals of the surrounding polygons
Computer_graphics_lighting
File format for 3D printing and scanning
triangles, each represented as follows: facet normal ni nj nk outer loop vertex v1x v1y v1z vertex v2x v2y v2z vertex v3x v3y v3z endloop endfacet where each
STL_(file_format)
Scale used to classify male pattern baldness
cases where hair loss occurs primarily from front to back without distinct vertex involvement. The classification was first introduced by James B. Hamilton
Norwood_scale
software to estimate the surface normal at any point on the mesh, by averaging the surface normals or vertex normals in the mesh data that describes the
Smoothing_group
Computer graphics rendering technique used to mimic the look of 2D animation
translated along their vertex normals in a vertex shader. After drawing the outline, back-face culling is set back to normal to draw the shading and
Cel_shading
Texture mapping technique
the normal map's normal vector with that of the eye (the viewpoint or camera) or the light vector. Since negative z values mean that the vertex is in
Normal_mapping
Computer programming paradigm
records within streams include: In graphics, each record may consist of vertex, normal, and color information for a triangle. In image processing, each record
Stream_processing
Object modeling method
popular Phong shading model. Some rendering systems use vertex normals instead of face normals to create a better-looking lighting system at the cost of
Polygonal_modeling
Figure formed by two rays meeting at a common point
line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and
Angle
graph G = (X+Y, E) is 2-colorable: each edge contains exactly one vertex of X and one vertex of Y, so e.g. X can be colored blue and Y can be colored yellow
Balanced_hypergraph
Shading algorithm in computer graphics
The first one is a so-called vertex shader and implements Phong shading, which is used to interpolate the surface normal between vertices. The second
Blinn–Phong_reflection_model
Generalization of depth-first search trees
depth-first search and connecting each vertex (other than the starting vertex of the search) to the earlier vertex from which it was discovered. The tree
Trémaux_tree
Organ in vertebrates that collects and stores urine from the kidneys before disposal
broad fundus (base), a body, an apex, and a neck. The apex (also called the vertex) is directed forward toward the upper part of the pubic symphysis, and from
Bladder
The slow vertex response (also called SVR or V potential) is an electrochemical signal associated with electrophysiological recordings of the auditory
Slow_vertex_response
Bézier surface created by control point interpolation
"Surface Construction with Near Least Square Acceleration based on Vertex Normals on Triangular Meshes" (PDF), in Ollila, Mark (ed.), SIGRAD 2002, pp
Bézier_triangle
Procedure to convert 3D scenes to 2D images
usually larger than available onboard memory. The geometry pipeline and the vertex pipeline are responsible for most of the operations with polygons. These
Graphics_pipeline
Monster and modular connection
moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James
Monstrous_moonshine
Graph defined from a mathematical group
element g {\displaystyle g} of G {\displaystyle G} is assigned a vertex: the vertex set of Γ {\displaystyle \Gamma } is identified with G . {\displaystyle
Cayley_graph
Interpolation method in computer graphics
the surface normal of each vertex in a polygonal 3D model is either specified for each vertex or found by averaging the surface normals of the polygons
Gouraud_shading
Central object in linear algebra; mapping vectors to vectors
{\displaystyle \mathbf {N} } is the three-dimensional unit vector for the vector normal of the plane. If the L2 norm of a {\displaystyle a} , b {\displaystyle b}
Transformation_matrix
3D printing technique
multiple files for the same 3D objects. OBJ vertices, texture mapping, vertex normals and faces No Multi-material support can be easily achieved with the
Multi-material_3D_printing
Measure of vertical distance
segment); In a rooted tree, the height of a vertex is the length of the longest downward path to a leaf from that vertex; In algebraic number theory, a "height
Height
Only rendering polygons facing towards the camera
anticommutative, defining the normal in terms of cross product means that the normal direction is dependent on the vertex order (winding): ( V 1 − V 0
Back-face_culling
Undirected, connected, and acyclic graph
Similarly, an external vertex (or outer vertex, terminal vertex or leaf) is a vertex of degree 1. A branch vertex in a tree is a vertex of degree at least
Tree_(graph_theory)
Data structure used in lightmapping
vertex lighting, lighting information is computed per vertex and stored in vertex color attributes. The two techniques may be combined, e.g. vertex color
Lightmap
Part of a fetus which will emerge first upon birth
other than a vertex presentation (with the top of the head first). Thus the various presentations are: cephalic presentation (head first): vertex (crown)—the
Presentation_(obstetrics)
Paper-and-pencil mathematical game
this cross ends up with a degree 1 vertex. Thus, throughout the game, every face has at least one degree 1 vertex. Yet, the number of degree 1 vertices
Sprouts_(game)
Pictorial representation of the behavior of subatomic particles
ending on a vertex. Lines in a Feynman diagram can now end either on an X vertex, or on an H vertex, and only one line enters an H vertex. The Feynman
Feynman_diagram
Standard for describing objects for additive manufacturing
curvature, a vertex can optionally contain a child element <normal> to specify desired surface normal at the location of the vertex. The normal should be
Additive manufacturing file format
Additive_manufacturing_file_format
Probability distribution
directional statistics, the projected normal distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution)
Projected_normal_distribution
Node-based visual programming language
introduced in version 4.0: Mesh – a collection of vertices and per-vertex normals, texture coordinates and colors in 3-space Interaction – a valueless
Quartz_Composer
Plane curve: conic section
symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along
Parabola
vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive)
List of uniform polyhedra by vertex figure
List_of_uniform_polyhedra_by_vertex_figure
Topics referred to by the same term
a dynamical system Hamiltonian path, a path in a graph that visits each vertex exactly once Hamiltonian matrix, a matrix with certain special properties
Hamiltonian
Symbols denoting astrological concepts
in the construction of a horoscope/natal chart Vertex Vx or Vx or 🜊 U+1F70A The vertex and anti-vertex are the points where the prime vertical intersects
Astrological_symbols
Computer graphics rendering technique
to other popular methods of lighting such as vertex lighting, which calculates illumination at each vertex of a 3D model and then interpolates the resulting
Per-pixel_lighting
Geometry of figures on the surface of a sphere
the sphere at the vertex A, or, equivalently, as the angle between the tangents of the great circle arcs where they meet at the vertex. The angles of proper
Spherical_trigonometry
graph, together with a family of monomorphisms of the edge groups into the vertex groups. There is a unique group, called the fundamental group, canonically
Graph_of_groups
Series of video cards
in various ways. The chip came equipped with over double the pixel and vertex pushing resources compared to the Radeon 9800 XT's R360 (a minor evolution
Radeon_R400_series
Measure of how strongly an optical system converges or diverges light
(sF) is the distance from the front focal point of the system (F) to the vertex of the first optical surface (S1). Some authors refer to this as "front
Focal_length
Vector with non-negative entries that add up to one
from the origin to the centroid coincides with the simplex’s normal vector. Each vertex is at an equal Euclidean distance ( n − 1 ) / n {\displaystyle
Probability_vector
Surface representing points of constant value within a volume
cubes. It retains a dual vertex within the voxel but no longer at the center. Dual contouring leverages the position and normal of where the surface crosses
Isosurface
called normal disks. Each normal disk is either a triangle which cuts off a vertex of the tetrahedron, or a quadrilateral which separates pairs of vertices
Normal_surface
Computer graphics technique
Often the displacement direction is also limited to the surface normal at the vertex. While conceptually similar, those polygons are usually a lot larger
Displacement_mapping
2005 video game
a per-pixel lighting model, which allows for complex lighting effects. Vertex, pixel, and high-level shaders are also featured in the game. Cutscenes
F.E.A.R._(video_game)
Part of the mathematical subject of group theory
The normal forms theorem immediately implies that the canonical homomorphisms Av → π1(A, T) are injective, so that we can think of the vertex groups
Bass–Serre_theory
File format designed to store three-dimensional data from 3D scanners
faces in total. After the header, the vertex and face data is listed. The vertex list contains position (x,y,z), normals (nx,ny,nz) and texture coordinates
PLY_(file_format)
Medical condition
showed atrophy, but four months after treatment the brain was seemingly normal again. As previously mentioned, chronic alcoholism is known to be associated
Cerebral_atrophy
Mathematical game
generalization of Kayles to graphs, each bowl “knocks down” (removes) a desired vertex and all its neighboring vertices,. Alternatively, this game can be viewed
Kayles
GPU for mobile devices, used by Nintendo on their 3DS consoles
programmable vertex processors which can work in parallel. One of those processors, the "primitive engine", can be used as either vertex processor or
PICA200
Directed graph representing overlaps between sequences of symbols
expressed as another vertex by shifting all its symbols by one place to the left and adding a new symbol at the end of this vertex, then the latter has
De_Bruijn_graph
Covering by shapes without overlaps or gaps
notation is the vertex configuration, which is simply a list of the number of sides of the polygons around a vertex. The square tiling has a vertex configuration
Tessellation
Statement in mathematical combinatorics
edge, (yz), is blue. Firstly, any given vertex will be the middle of either 0 × 5 = 0 (all edges from the vertex are the same colour), 1 × 4 = 4 (four are
Ramsey's_theorem
Fetal position in the womb
delivered first (fetal presentation), there are many possible positions: Vertex presentation with longitudinal lie: Breech presentation with longitudinal
Position_(obstetrics)
Graph algorithm
preorder numbers of the vertices. When the depth-first search reaches a vertex v, the algorithm performs the following steps: Set the preorder number of
Path-based strong component algorithm
Path-based_strong_component_algorithm
Marked objects for finding random numbers
and three () faces to share a vertex. The faces of a die may be placed clockwise or counterclockwise about this vertex. If the one (), two (), and three
Dice
Directed graph representing a Boolean expression
composed of vertex set V and directed edge set E. Each vertex in V represents the truth status of a Boolean literal, and each directed edge from vertex u to
Implication_graph
Complements of perfect graphs are perfect
-vertex bipartite graphs, a minimum clique cover takes the form of a maximum matching together with an additional clique for every unmatched vertex, with
Perfect_graph_theorem
Problem of determining if a Boolean formula could be made true
formula consisting of c clauses, the corresponding graph consists of a vertex for each literal, and an edge between each two non-contradicting literals
Boolean satisfiability problem
Boolean_satisfiability_problem
In mathematics, straight line touching a plane curve without crossing it
two circular arcs meet at a sharp point (a vertex) then there is no uniquely defined tangent at the vertex because the limit of the progression of secant
Tangent
Graphics programming language
Previous vertex shading languages (in no particular order) for OpenGL include EXT_vertex_shader, NV_vertex_program, the aforementioned ARB_vertex_program
Shading_language
n-vertex cubic graph? The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of lens to improve visual perception
lens. Vertex distance is the space between the front of the eye and the back surface of the lens. In glasses with powers beyond ±4.00D, the vertex distance
Corrective_lens
Multi-dimensional generalization of triangle
k-simplex may be constructed from a regular (k − 1)-simplex by connecting a new vertex to all original vertices by the common edge length. The standard simplex
Simplex
Nerve of the head
further to supply the skin along the posterior part of the scalp to the vertex. It supplies sensation to the scalp at the top of the head, over the ear
Greater_occipital_nerve
Graph with same nodes as but complementary connections to another
defined by adding a self-loop to every vertex that does not have one in G, removing its self-loop from every vertex that has one in G, and otherwise using
Complement_graph
Task of computing complete subgraphs
single vertex or even the empty set), grow the current clique one vertex at a time by looping through the graph's remaining vertices. For each vertex v that
Clique_problem
Brand name by ATI
cubic Bezier patch and a separate normal interpolant derived from the triangle's existing vertex positions and normals; in OpenGL, ATI exposed it through
ATI_TruForm
Topics referred to by the same term
part of a person, as opposed to being "normal" Off-center, in geometry Eccentricity (graph theory) of a vertex in a graph Eccentricity (mathematics),
Eccentricity
Computer graphics polygon very small relative to the image being rendered
might fill each micropolygon with a single color or assign colors on a per-vertex basis. Shaders that operate on micropolygons can process an entire grid
Micropolygon
Algebraic variety containing an algebraic torus
P} be a polytope. For any vertex v {\displaystyle v} of P {\displaystyle P} , the normal cone of P {\displaystyle P} at vertex v {\displaystyle v} is the
Toric_variety
Midline joint of the skull
the bregma, and the vertex of the skull. The bregma is formed by the intersection of the sagittal and coronal sutures. The vertex is the highest point
Sagittal_suture
Non-perturbative approach to quantum field theory
a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal
Operator_product_expansion
Uniform Euclidean 3D tessellations and their duals
the Platonic, Archimedean, and Catalan tiling of the plane. The singular vertex figure of an architectonic tessellation is the dual of the cell of the corresponding
Architectonic and catoptric tessellation
Architectonic_and_catoptric_tessellation
Interior channel of a wind instrument
diameter—the cone's vertex. However, actual instrument bores approximate a frustum of a cone. The wavelength produced by the first normal mode is approximately
Bore_(wind_instruments)
Type of polytope in mathematics
combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given any positive integer n, every lattice
Normal_polytope
Parallel version of breadth-first search algorithm
frontier. At the beginning of the BFS algorithm, a given source vertex s is the only vertex in the frontier. All direct neighbors of s are visited in the
Parallel_breadth-first_search
Triangular array of the binomial coefficients
a vertex V, there is one vertex at distance 0 from V (that is, V itself), three vertices at distance 1, three vertices at distance √2 and one vertex at
Pascal's_triangle
Screen-space shading technique
shading technique that is performed on a second rendering pass, after the vertex and pixel shaders are rendered. It was first suggested by Michael Deering
Deferred_shading
Directed graph isomorphic to its own transpose graph
vertices of G, satisfying the following properties: For every vertex v, σ(v) ≠ v, For every vertex v, σ(σ(v)) = v, For every edge (u,v), (σ(v),σ(u)) must also
Skew-symmetric_graph
Graph whose induced subgraphs preserve distance
existing vertex of the graph. Replace any vertex of the graph by a pair of vertices, each of which has the same set of neighbors as the replaced vertex. The
Distance-hereditary_graph
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