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  2. Computer representation of surfaces - Wikipedia

    en.wikipedia.org/wiki/Computer_representation_of...

    These are generalizations of the x and y Cartesian coordinate lines in the plane coordinate system and of the meridians and circles of latitude on a spherical coordinate system. Open surfaces are not closed in either direction. This means moving in any direction along the surface will cause an observer to hit the edge of the surface.

  3. Position (geometry) - Wikipedia

    en.wikipedia.org/wiki/Position_(geometry)

    In three dimensions, any set of three-dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used. Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates:

  4. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...

  5. Vector fields in cylindrical and spherical coordinates

    en.wikipedia.org/wiki/Vector_fields_in...

    Vectors are defined in cylindrical coordinates by (ρ, φ, z), where ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:

  6. Orthogonal coordinates - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_coordinates

    A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...

  7. Homogeneous coordinates - Wikipedia

    en.wikipedia.org/wiki/Homogeneous_coordinates

    Homogeneous coordinates are not uniquely determined by a point, so a function defined on the coordinates, say (,,), does not determine a function defined on points as with Cartesian coordinates. But a condition f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0} defined on the coordinates, as might be used to describe a curve, determines a condition ...

  8. Orthographic projection - Wikipedia

    en.wikipedia.org/wiki/Orthographic_projection

    Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.

  9. UVW mapping - Wikipedia

    en.wikipedia.org/wiki/UVW_mapping

    The UVW mapping is suitable for painting an object's surface based on a solid texture. This allows a marble texture to wrap a vase to appear as if it were carved from actual marble. "UVW", like the standard Cartesian coordinate system, has three dimensions; the third dimension allows texture maps to wrap in complex ways onto irregular surfaces ...