3D projection

projectiongraphical projection3D
B_z is the focal length—the axial distance from the camera center to the image plane. A_z is the subject distance. 3D computer graphics. Camera matrix. Computer graphics. Cross section. Curvilinear perspective. Cutaway. Descriptive geometry. Engineering drawing. Exploded-view drawing. Graphics card. Homogeneous coordinates. Homography. Map projection (including Cylindrical projection). Multiview projection. Perspective (graphical). Plan (drawing). Technical drawing. Texture mapping. Transform and lighting. Viewing frustum. Virtual globe.

Picture plane

integrity of the picture planeperspective planephotographical plane
Morehead Jr. (1911) Perspective and Projective Geometries: A Comparison from Rice University. Perspective projection. Projection plane. Image plane.

Orthographic projection

An orthographic projection map is a map projection of cartography. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges. The orthographic projection has been known since antiquity, with its cartographic uses being well documented.

Projective geometry

projectiveprojective geometriesProjection
The first geometrical properties of a projective nature were discovered during the 3rd century by Pappus of Alexandria. Filippo Brunelleschi (1404–1472) started investigating the geometry of perspective during 1425 (see the history of perspective for a more thorough discussion of the work in the fine arts that motivated much of the development of projective geometry). Johannes Kepler (1571–1630) and Gérard Desargues (1591–1661) independently developed the concept of the "point at infinity". Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing points to include the case when these are infinitely far away.


z-bufferdepth bufferdepth
The range of depth values in camera space to be rendered is often defined between a and value of z. After a perspective transformation, the new value of z, or z', is defined by: After an orthographic projection, the new value of z, or z', is defined by: where z is the old value of z in camera space, and is sometimes called w or w'. The resulting values of z' are normalized between the values of -1 and 1, where the plane is at -1 and the plane is at 1. Values outside of this range correspond to points which are not in the viewing frustum, and shouldn't be rendered. Typically, these values are stored in the z-buffer of the hardware graphics accelerator in fixed point format.

Shadow mapping

shadowsshadow mapCascaded Shadow Maps
For a point light source, the view should be a perspective projection as wide as its desired angle of effect (it will be a sort of square spotlight). For directional light (e.g., that from the Sun), an orthographic projection should be used. From this rendering, the depth buffer is extracted and saved. Because only the depth information is relevant, it is common to avoid updating the color buffers and disable all lighting and texture calculations for this rendering, in order to save drawing time. This depth map is often stored as a texture in graphics memory.

Cube mapping

cube mapcube mapsCube-mapped
Another application which found widespread use in video games is projective texture mapping. It relies on cube maps to project images of an environment onto the surrounding scene; for example, a point light source is tied to a cube map which is a panoramic image shot from inside a lantern cage or a window frame through which the light is filtering. This enables a game developer to achieve realistic lighting without having to complicate the scene geometry or resort to expensive real-time shadow volume computations. A cube texture indexes six texture maps from 0 to 5 in order Positive X, Negative X, Positive Y, Negative Y, Positive Z, Negative Z.

Virtual camera system

third-personthird-person perspectivethird-person view
The Walkthrough Project at the University of North Carolina at Chapel Hill produced a number of physical input devices for virtual camera view control including dual three-axis joysticks and a billiard-ball shaped prop known as the UNC Eyeball that featured an embedded six-degree of freedom motion tracker and a digital button. Camera matrix. Game engine. Virtual cinematography. First-person (video games).

Parallax occlusion mapping

Parallax occlusion mapping is used to procedurally create 3D definition in textured surfaces, using a displacement map (similar to a topography map) instead of through the generation of new geometry. This allows developers of 3D rendering applications to add 3D complexity in textures, which correctly change relative to perspective and with self occlusion in real time (self-shadowing is additionally possible), without sacrificing the processor cycles required to create the same effect with geometry calculations. Parallax occlusion mapping was first published in 2005 by Zoe Brawley and Natalya Tatarchuk in ShaderX3.

3D rendering

rendering3D acceleration3D
A simple example of shading is texture mapping, which uses an image to specify the diffuse color at each point on a surface, giving it more apparent detail. Some shading techniques include: Transport describes how illumination in a scene gets from one place to another. Visibility is a major component of light transport. The shaded three-dimensional objects must be flattened so that the display device - namely a monitor - can display it in only two dimensions, this process is called 3D projection. This is done using projection and, for most applications, perspective projection.

List of computer graphics and descriptive geometry topics

Reverse perspective. Scan line rendering. Scrolling. Technical drawing. Texture mapping. Trimetric projection. Vanishing point. Vector graphics. Vector graphics editor. Vertex shaders. Volume rendering. Voxel. List of geometry topics. List of graphical methods.

Rendering (computer graphics)

Some are integrated into larger modeling and animation packages, some are stand-alone, some are free open-source projects. On the inside, a renderer is a carefully engineered program, based on a selective mixture of disciplines related to: light physics, visual perception, mathematics, and software development. In the case of 3D graphics, rendering may be done slowly, as in pre-rendering, or in realtime. Pre-rendering is a computationally intensive process that is typically used for movie creation, while real-time rendering is often done for 3D video games which rely on the use of graphics cards with 3D hardware accelerators.

3D computer graphics

3D3D graphicsthree-dimensional
. • Graphics and software • Glossary of computer graphics • Comparison of 3D computer graphics software • Graphics processing unit (GPU) • Graphical output devices • List of 3D computer graphics software • List of 3D modeling software • List of 3D rendering software • Real-time computer graphics • Reflection (computer graphics) • Rendering (computer graphics) • Fields of use • 3D data acquisition and object reconstruction • 3D motion controller • 3D projection on 2D planes • 3D reconstruction • 3D reconstruction from multiple images • Anaglyph 3D • Computer animation • Computer vision • Digital geometry • Digital image processing • Game development tool • Game engine • Geometry pipelines • Geometry

UV mapping

UVUV unwrappingUVs
UV mapping is the 3D modelling process of projecting a 2D image to a 3D model's surface for texture mapping. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y" and "Z" are already used to denote the axes of the 3D object in model space. UV texturing permits polygons that make up a 3D object to be painted with color (and other surface attributes) from an ordinary image. The image is called a UV texture map. The UV mapping process involves assigning pixels in the image to surface mappings on the polygon, usually done by "programmatically" copying a triangular piece of the image map and pasting it onto a triangle on the object.

Sprite (computer graphics)

Modern GPU hardware can mimic sprites with two texture-mapped triangles or specific primitives such as point sprites. Some hardware makers used terms other than sprite. Player/Missile Graphics was a term used by Atari, Inc. for hardware-generated sprites in the company's early coin-op games, the Atari 2600 and 5200 consoles, and the Atari 8-bit computers. The term reflected the usage for both characters ("players") and smaller associated objects ("missiles") that share the same color. Movable Object Block, or MOB, was used in MOS Technology's graphics chip literature (data sheets, etc.)

Reverse perspective

Byzantine perspectiveinverse perspectivereversible perspective
Technically, the vanishing points are placed outside the painting with the illusion that they are "in front of" the painting. The name Byzantine perspective comes from the use of this perspective in Byzantine and Russian Orthodox icons; it is also found in the art of many pre-Renaissance cultures, and was sometimes used in Cubism and other movements of modern art, as well as in children's drawings.

Graphics processing unit

GPUGPUsgraphics processor
GPUs were initially used to accelerate the memory-intensive work of texture mapping and rendering polygons, later adding units to accelerate geometric calculations such as the rotation and translation of vertices into different coordinate systems. Recent developments in GPUs include support for programmable shaders which can manipulate vertices and textures with many of the same operations supported by CPUs, oversampling and interpolation techniques to reduce aliasing, and very high-precision color spaces.

Descriptive geometry

Projective geometry. Graphical projection. Orthographic projection. Axonometric projection. Isometric projection. Dimetric projection. Trimetric projection. Orthogonal projection. Oblique projection. Perspective projection, Perspective (graphical). Technical drawing. Engineering drawing.


pixel shadervertex shadershaders
Vertex shaders describe the traits (position, texture coordinates, colors, etc.) of a vertex, while pixel shaders describe the traits (color, z-depth and alpha value) of a pixel. A vertex shader is called for each vertex in a primitive (possibly after tessellation); thus one vertex in, one (updated) vertex out. Each vertex is then rendered as a series of pixels onto a surface (block of memory) that will eventually be sent to the screen. Shaders replace a section of the graphics hardware typically called the Fixed Function Pipeline (FFP), so-called because it performs lighting and texture mapping in a hard-coded manner. Shaders provide a programmable alternative to this hard-coded approach.

Mathematics and art

mathematical artmathematics of artartistic and imaginative pursuit
These, such as the rhombicuboctahedron, were among the first to be drawn to demonstrate perspective by being overlaid on top of each other. The work discusses perspective in the works of Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano. Da Vinci studied Pacioli's Summa, from which he copied tables of proportions. In Mona Lisa and The Last Supper, Da Vinci's work incorporated linear perspective with a vanishing point to provide apparent depth. The Last Supper is constructed in a tight ratio of 12:6:4:3, as is Raphael's The School of Athens, which includes Pythagoras with a tablet of ideal ratios, sacred to the Pythagoreans.

Computer graphics

Ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane. The technique is capable of producing a very high degree of photorealism; usually higher than that of typical scanline rendering methods, but at a greater computational cost. Texture mapping. Texture mapping is a method for adding detail, surface texture, or colour to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Dr Edwin Catmull in 1974. A texture map is applied (mapped) to the surface of a shape, or polygon. This process is akin to applying patterned paper to a plain white box.


light maplight mappinglightmapping
Texture mapping. Baking (computer graphics).