Geometric primitive
Encyclopedia
The term geometric primitive in computer graphics
and CAD systems is used in various senses, with the common meaning of the simplest (i.e. 'atomic' or irreducible) geometric objects that the system can handle (draw, store). Sometimes the subroutine
s that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segment, which were all that early vector graphics
systems had.
In constructive solid geometry
, primitives are simple geometric
shapes such as a cube, cylinder
, sphere
, cone
, pyramid
, torus
.
Modern 2D computer graphics
systems may operate with primitives which are lines (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles).
A common set of two-dimensional primitives includes lines, points, and polygon
s, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles. All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as Bézier curve
s, circle
s, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes.
Commonly used geometric primitives include:
Note that in 3D applications basic geometric shapes and forms are considered to be primitives rather than the above list. Such shapes and forms include:
These are considered to be primitives in 3D modelling because they are the building blocks for many other shapes and forms. A 3D package may also include a list of extended primitives which are more complex shapes that come with the package. For example, a teapot
is listed as a primitive in 3D Studio Max
.
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
and CAD systems is used in various senses, with the common meaning of the simplest (i.e. 'atomic' or irreducible) geometric objects that the system can handle (draw, store). Sometimes the subroutine
Subroutine
In computer science, a subroutine is a portion of code within a larger program that performs a specific task and is relatively independent of the remaining code....
s that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segment, which were all that early vector graphics
Vector graphics
Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon, which are all based on mathematical expressions, to represent images in computer graphics...
systems had.
In constructive solid geometry
Constructive solid geometry
Constructive solid geometry is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine objects...
, primitives are simple geometric
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
shapes such as a cube, cylinder
Cylinder (geometry)
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...
, sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
, cone
Cone (geometry)
A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...
, pyramid
Pyramid (geometry)
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base....
, torus
Torus
In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...
.
Modern 2D computer graphics
2D computer graphics
2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models and by techniques specific to them...
systems may operate with primitives which are lines (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles).
A common set of two-dimensional primitives includes lines, points, and polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
s, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles. All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as Bézier curve
Bézier curve
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case....
s, circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes.
Commonly used geometric primitives include:
- pointPoint (geometry)In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
s - linesLine (mathematics)The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
and line segmentLine segmentIn geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...
s - planePlane (mathematics)In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...
s - circleCircleA circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s and ellipseEllipseIn geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
s - triangleTriangleA triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
s and other polygonPolygonIn geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
s - spline curvesSpline (mathematics)In mathematics, a spline is a sufficiently smooth piecewise-polynomial function. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher...
Note that in 3D applications basic geometric shapes and forms are considered to be primitives rather than the above list. Such shapes and forms include:
- sphereSphereA sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
s - cubeCubeIn geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
s or boxBoxBox describes a variety of containers and receptacles for permanent use as storage, or for temporary use often for transporting contents. The word derives from the Greek πύξος , "box, boxwood"....
es - toroidToroidToroid may refer to*Toroid , a doughnut-like solid whose surface is a torus.*Toroidal inductors and transformers which have wire windings on circular ring shaped magnetic cores.*Vortex ring, a toroidal flow in fluid mechanics....
s - cylinderCylinder (geometry)A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...
s - pyramidPyramid (geometry)In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base....
s
These are considered to be primitives in 3D modelling because they are the building blocks for many other shapes and forms. A 3D package may also include a list of extended primitives which are more complex shapes that come with the package. For example, a teapot
Utah teapot
The Utah teapot or Newell teapot is a 3D computer model which has become a standard reference object in the computer graphics community. It is a mathematical model of an ordinary teapot of fairly simple shape, which appears solid, cylindrical and partially convex...
is listed as a primitive in 3D Studio Max
3D Studio Max
Autodesk 3ds Max, formerly 3D Studio MAX, is for making 3D animations. It was developed and produced by Autodesk Media and Entertainment. It has modeling capabilities, a flexible plugin architecture and can be used on the Microsoft Windows platform. It's frequently used by video game developers, TV...
.