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Topic: Vertex (geometry)

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Summary of 3D Tests of 101 Video Cards Manufactured in 1999-2004 (October, 2004) Hercules 3D Prophet 9600 256MB DDR 128bit, 325/200 (400) MHz (4 pixel pipelines with one texture unit each (up to 16 textures at a pass), DirectX 9.0 support, Shaders 2.0, hardware processing of geometry and lighting is based on two vertex pipelines) Galaxy GeForce FX 5700LE 128MB 128bit, 300/200 (400) MHz (4 pixel pipelines with one texture unit each (up to 16 textures at a pass), DirectX 9.0 support, Shaders 2.0+, hardware processing of geometry and lighting is based on three vertex pipelines) ASUS A9600SE 128MB DDR 64bit, 325/200 (400) MHz (4 pixel pipelines with one texture unit each (up to 16 textures at a pass), DirectX 9.0 support, Shaders 2.0, hardware processing of geometry and lighting is based on two vertex pipelines) www.digit-life.com /articles2/over2k4/index_2003.html

Defect (geometry) - Wikipedia, the free encyclopedia In geometry, the defect of a vertex of a polyhedron is the amount by which the sum of the angles of the faces at the vertex falls short of a full circle. The defect of any of the vertices of a regular dodecahedron (in which three regular pentagons meet at each vertex) is 36°, or π/5 radians, or 1/10 of a circle. It is tempting to think (and has even been stated in geometry textbooks) that every non-convex polyhedron has some vertices whose defect is negative. en.wikipedia.org /wiki/Defect_(geometry)   (372 words)

The angle defect of a polyhedron The angle defect at a vertex of a polygon is defined to be You can visualize the angle defect by cutting along an edge at that vertex, and then flattening out a neighborhood of the vertex into the plane. Up: Geometry and the Imagination Previous: Course projects geom.math.uiuc.edu /docs/education/institute91/handouts/node18.html   (163 words)

PinkMonkey.com Geometry Study Guide - 2.4 Altitude, Median and Angle Bisector A line segment from the vertex of a triangle to the midpoint of the side opposite to it is called a median. A line segment from the vertex to the opposite side such that it bisects the angle at the vertex is called as angle bisector. All three medians always meet inside the triangle irrespective of the type of triangle. www.pinkmonkey.com /studyguides/subjects/geometry/chap2/g0202401.asp   (299 words)

VR-ZONE HARDWARE Zooming in on the geometry pipelines, G70 has two more vertex shaders than the NV40/45 with a total of 8 vertex shaders handling geometry processing. The advantage of a unified shader approach is unproven yet but generally it should benefit the geometry processing more since vertex shader units are always lesser in number than pixel shader units. On the NV40, the pixel shader pipeline consists of two shader units with a texture unit in between and each shader unit can process 4 ops per pixel which translate to up to 8 ops per pixel. www.vr-zone.com /?i=2367&p=1   (299 words)

Platform Comparison - A "Genuine" GC, PS2, Xbox Comparison The CPU can send static vertex meshes to the vertex shader or standard TandL pipelines to be processed along with the tessellated dynamic geometry, or no dynamic geometry could be used at all. The vertex shaders and standard TandL pipeline can operate on the vertices ouputed by the hardware surface tessellator, but not on the surface control points. No hardware dynamic surface generation supported, geometry rendering is done on the CPU. forum.pcvsconsole.com /viewpost.php?pid=33623   (299 words)

Neowin.net -> GeForce 6800 May Deliver Lower Performance The difference in geometry performance submitted by Leadtek is higher than the difference in clock-speeds between various models. The GeForce 6800 Ultra packs in 16 pixel pipelines and 6 vertex pipelines, the GeForce 6800 GT reportedly integrates the same amount of pixel and vertex processors. Previously ATI was renowned for disabling defective pixel pipelines in cut-down versions of its processors, now NVIDIA is seemingly able to deactivate both pixel and vertex processors. www.neowin.net /forum/index.php?showtopic=210610   (299 words)

Digital Cinema Arts-Real Flow Geometry ROP/IFD "Vertex Mode" will output geometry for each frame, which allows geometry deformations to appear in the SD file. The Real Flow SD ROP interface is nearly identical to any other Houdini ROP with the exception of having a toggle for "Vertex Mode" and the output filename is specified in the "SD File Name" field instead of the "Output Picture" field. The Real Flow SD file has a feature called "Matrix or Vertex Mode". www.digitalcinemaarts.com /dev/real_flow/RF_ROP-IFD.html   (299 words)

Math Forum - geometry.puzzles A point is selected inside a rectangle such that its distance from one vertex is 11 cm, its distance from the opposite vertex is 12 cm, and its distance from a third vertex is 3 cm. Projective Geometry Question (S. I have the following problem to solve: We have an observation point p and plane P. The minimum distance between p & P is given : d. My geometry book says that, for two triangles to be congruent, you must prove that the hypotenuse AND one leg are congruent. forum.swarthmore.edu /~sarah/HTMLthreads/geopuzzles.descriptions.html   (3830 words)

VRML 2.0 Geometry Import Converter Vertex normals, vertex texture coordinates, vertex colors, per-face colors and material assignments are supported for the indexed face set geometry. If geometry is DEFd then USEd more than once in the VRML file (ie: the geometry is instantiated multiple times), then this converter will create one object definition internally and create multiple instances of the object definition (to replicate the behaviour of VRML). Level of detail allows varying levels of geoemtry detail to be displayed in a VRML browser; geometry closer to the camera will use the highest level of detail and geometry far from the camera will use the lowest level of detail. www.okino.com /conv/imp_vrml.htm   (3041 words)

Algebra Graph Overview VMP is a class library which comprises namespaces for vetcors and matrices, linear algebra, graph theory, geometry and finite element analysis and more. Dijkstra continued applying his method in a number of diverse areas: coordinate geometry, linear algebra, graph theory, designs of sequential and distributed programs, and many others. Abstract algebra Number theory Algebraic geometry Group theory Monoids Analysis Topology Linear algebra Graph theory Universal algebra Category theory Order theory [edit] Space These topics tend to... www.algebraz.com /AlgebraGraph   (3041 words)

Triangle - Wikipedia, the free encyclopedia A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base. en.wikipedia.org /wiki/Triangle_(geometry)   (3041 words)

MSN Encarta - Triangle (geometry) A capital letter is customarily used to designate a vertex of a triangle, the angle at that vertex, or the measure of the angle in angular units; the corresponding lower case letter designates the side opposite the angle or its length in linear units. A Euclidean plane triangle has three interior angles (the word interior is often omitted), each formed by two adjacent sides, as ÐCAB in Fig. For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle. encarta.msn.com /encyclopedia_761563143/Triangle_(geometry).html   (3041 words)

Median (geometry) - Wikipedia, the free encyclopedia The three medians intersect in the triangle's centroid or center of mass, and two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side. In a triangle, a median is a line joining a vertex to the midpoint of the opposite side. It divides the triangle into two parts of equal area. en.wikipedia.org /wiki/Median_(geometry)   (124 words)

GEOMETRY - LoveToKnow Article on GEOMETRY Pythagoras (q.v.), seeking the key of the universe in arithmetic and geometry, investigated logically the principles underlying the, known propositions; and this resulted in the formulation of definitions, axioms and postulates which, in addition to founding a science of geometry, permitted a crystallization, fractional, it is true, of the amorphous collection of material at hand. Pythagorean geometry was essentially a geometry of areas and solids; its goal was the regular solids the tetrahedron, cube, octahedron, dodecahedron and icosahedronwhich symbolized the five elements of Greek cosmology. The line which bisects an exterior angle of a triangle divides the opposite side externally in the ratio of the other sides; and conversely, if a line through the vertex of a triangle divide the base externally in the ratio of the sides, then it bisects an exterior angle at the vertex of the triangle. www.1911encyclopedia.org /G/GE/GEOMETRY.htm   (21277 words)

Cone - Wikipedia, the free encyclopedia Also in geometry, the cone of an arbitrary set X means the union of all line segments connecting a fixed point to points of X. In graph theory, a cone graph is a graph with a universal vertex (a vertex that is connected to all others vertices). In ceramics manufacture, a pyrometric cone is a conical or pyramidal mineral stick that is used to gauge the temperature of an oven. www.wikipedia.org /wiki/Cone   (21277 words)

Geometry: Class Hierarchy/Data Structures The Geometry Domain Class (GD) is derived from the GB class and further defines primitives with trimmed surface and surface domain information. The Geometry Utility Class (GU) is derived from GEO and contains a number of functions for creating and manipulating primitives and points. Primitives are contained with a geometry detail primitive list. accad.osu.edu /~pete/Houdini/html/geometry/class.html   (21277 words)

SGI TPL (IRIX 6.5: Developer/Perf_PG - Chapter 8. Geometry) The way to get more than one primitive to refer to the same vertex is to use an index; three vertices of three primitives use the same index which points to the same vertex information. The choice of using indexed or sequential attributes applies to all of the primitives in a pfGeoSet; that is, all of the primitives within one pfGeoSet must be referenced sequentially or by index; you cannot mix the two. Table 8-2 lists the primitive type tokens, the primitive types that they represent, and the number of vertices in a coordinate list for that type of primitive. techpubs.sgi.com /library/tpl/cgi-bin/getdoc.cgi?coll=0650&db=bks&fname=/SGI_Developer/Perf_PG/ch08.html   (21277 words)

Welcome to AnandTech.com [ Article: ATI Radeon X800 Pro and XT Platinum Edition: R420 Arrives] The point of the vertex pipeline in any GPU is to take geometry data, manipulate it if needed (with either fixed function processes, or a vertex shader program), and project all of the 3D data in a scene to 2 dimensions for display. With early z, as data emerges from the geometry processing portion of the GPU, it is possible to skip further rendering large portions of the scene that are occluded (or covered) by other geometry. In this case, the number of internal pipeline stages in each pixel pipeline, and the ability of the hardware to hide the latency of a texture fetch are of the utmost importance. www.anandtech.com /printarticle.html?i=2044   (21277 words)

5.1 Triangles The median is the segment joining a vertex to the midpoint of the opposite side. be the lengths of the altitude, bisector and median originating in vertex C, let r and R be as usual the radii of the inscribed and circumscribed circles, and let s=½(a+b+c). The point of intersection of the medians is the center of mass of the triangle (considered as an area in the plane). www.geom.uiuc.edu /docs/reference/CRC-formulas/node22.html   (704 words)

discreet If you define one vertex as blue and the other as red, all the points between these 2 vertices will be assigned to a color based on a gradient between these two colors. Understanding the lighting effects created by Lightscape using vertex coloring. Now, let's apply the vertex coloring on real situations. www.discreet.com /support/lightscape/faq/answer.php3?prod=lightscape&id=524   (704 words)

Lecture_5 Now _Total Angle Defect_(P) equals the sum of all the _Local Angle Defects_ at each vertex, each of which is 360 minus the sum of the angles which meet at the vertex. This makes it a remarkable fact that _Total Angle Defect_ depends not an the conformal geometry of a polyhedron, nor even on its combinatorial geometry, but *only* on its topology. The eight corners of the tunnel have _Local Angle Defect_ equal 360- (90 + 90 + 270) = -90 degrees (You'll find the 270 degree angle on the top or bottom of the cube and the 90 degree angles on the walls of the tunnel.) Thus, in this, case the _Total Angle Defect_ equals 0. www.math.unh.edu /~dvf/Pathways/Lecture_5   (1253 words)

Java Gallery: Hyperbolic Triangles One of the most surprising facts in hyperbolic geometry is that there is an upper limit to the possible area a triangle can have, even though there is not an upper limit to the lengths of the sides of the triangle. In hyperbolic geometry, the sum of the angles of a triangle is always less than 180 degrees (PI radians). As you drag a vertex to infinity (the boundary of the disk), the angle at that vertex goes to zero. www.geom.uiuc.edu /java/triangle-area   (275 words)

Tetrahedron - Wikipedia, the free encyclopedia A regular tetrahedron can be embedded inside a cube in two ways such that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces. Taking both tetrahedra within a single cube gives a regular polyhedral compound called the stella octangula, whose interior is an octahedron. The volume of this tetrahedron is 1/3 the volume of the cube. www.lexington-fayette.us /project/wikipedia/index.php/Tetrahedron   (275 words)

Student Abstracts: LBNL - Nuclear Science It is important to characterize the signal to noise, readout time, and resolution on several different pixel sizes so that the vertex detector can be optimized for cost and speed. By replicating the experiment with activation foils that are not radioactive, using identical geometry the neutron flux can be evaluated and energy information can be obtained. To achieve this goal, STAR is building a vertex detector consisting of a new technology — active pixel sensors. www.scied.science.doe.gov /scied/Abstracts2004/LBNLns.htm   (2778 words)

An Interactive, Parallel Geometry Viewer Unlike most geometry formats, TVF files specify vertex connectivity information (triangles) first, followed by the vertex coordinates. This reverse ordering simplifies the algorithms used to distribute the geometry data uniformly across all of the processors. By rendering the data in-place on the parallel machine, the need to copy large files to a remote workstation for rendering and display is eliminated. www.compsci.wm.edu /~tom/SC94/TVFView.html   (372 words)

Round Triangles: medians In the metric geometries of Euclidean, hyperbolic, and elliptic geometries, a median can be defined as a straight line that connects a vertex of the triangle to the midpoint of the opposite side. In order to find the median from vertex A to the opposite side BC, we'll construct two circles which will act as lines parallel to the sides AB and AC, and connect A to their intersection. Inversive geometry is not a metric geometry, so midpoints cannot be defined. aleph0.clarku.edu /~djoyce/java/round/round2.html   (346 words)

The Euler Line of a Triangle It can be shown that the centroid trisects the medians, that is to say, the distance from a vertex to the centroid G is twice the distance from the centroid to the opposite side of the triangle. A line connecting a vertex of the triangle to the midpoint of the opposite side is called a median of the triangle. It's amazing how much geometry there is in the lowly triangle! aleph0.clarku.edu /~djoyce/java/Geometry/eulerline.html   (929 words)

Math Forum - Ask Dr. Math Archives: Middle School Higher-Dimensional Geometry Our 4th grade math textbook defines a cone as "A solid figure with one circular face and one vertex." This sounds reasonable until you read the textbook's definitions for face, edge, and vertex. If space is curved and Euclidean geometry doesn't apply, doesn't that mean that the value of pi changes and can sometimes be rational? My son was asked "how many edges are there on a solid cylinder?" on a recent math examination. mathforum.org /library/drmath/sets/mid_3d.html   (756 words)

Math Forum - Ask Dr. Math Archives: High School Higher-Dimensional Geometry Our 4th grade math textbook defines a cone as "A solid figure with one circular face and one vertex." This sounds reasonable until you read the textbook's definitions for face, edge, and vertex. In my Geometry class we read the book, Sphereland. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2". mathforum.org /library/drmath/sets/high_3d.html   (756 words)

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