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trunk/blender_docs/manual/glossary/math.rst
| Property | Old Value | New Value |
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| svn:eol-style | null | LF \ No newline at end of property |
| **** | |||||
| Math | |||||
| **** | |||||
| .. For writing style guide, see: :doc:`/about/contribute/style_guides/writing_guide` | |||||
| If you add new entries, keep the alphabetical sorting! | |||||
| .. glossary:: | |||||
| Interpolation | |||||
| Method of calculating new data between points of known value, like :term:`keyframes <keyframe>`. | |||||
| Boolean | |||||
| A type of logic dealing with binary true/false states. | |||||
| See also :doc:`Boolean Modifier </modeling/modifiers/generate/booleans>`. | |||||
| Clamp | |||||
| Clamping | |||||
| Limits a variable to a range. The values over or under the range are set | |||||
| to the constant values of the ranges minimum or maximum. | |||||
| Geometry | |||||
| ======== | |||||
| .. glossary:: | |||||
| Axis | |||||
| A reference line which defines coordinates along one cardinal direction in n-D space. | |||||
| Axis Angle | |||||
| Rotation method where X, Y, and Z correspond to the axis definition, | |||||
| while W corresponds to the angle around that axis, in radians. | |||||
| Bevel | |||||
| The operation to chamfer or bevel edges of an object. | |||||
| Bounding Box | |||||
| The box that encloses the shape of an object. The box is aligned with the local space of the object. | |||||
| Concave face | |||||
| Face in which one vertex is inside a triangle formed by other vertices of the face. | |||||
| Convex face | |||||
| Face where, if lines were drawn from each vertex to every other vertex, all lines would remain in the face. | |||||
| Opposite of a :term:`concave face`. | |||||
| Coplanar | |||||
| Refers to any set of elements that are all aligned to the same 2D plane in 3D space. | |||||
| Edge | |||||
| Straight segment (line) that connects two :term:`vertices <vertex>`, and can be part of a :term:`face`. | |||||
| Edge Loop | |||||
| Chain of :term:`edges <edge>` belonging to consecutive :term:`quads <quad>`. | |||||
| An edge loop ends at a pole or a boundary. Otherwise, it is cyclic. | |||||
| Edge Ring | |||||
| Path of all :term:`edges <edge>` along a :term:`face loop` that share two faces belonging to that loop. | |||||
| Euler | |||||
| Euler Rotation | |||||
| Rotation method where rotations applied on each X, Y, Z axis component. | |||||
| Face | |||||
| Mesh element that defines a piece of surface. It consists of three or more :term:`edges <edge>`. | |||||
| Face Loop | |||||
| Chain of consecutive :term:`quads <quad>`. | |||||
| A face loop stops at a :term:`triangle` or :term:`N-gon` (which do not belong to the loop), or at a boundary. | |||||
| Otherwise, it is cyclic. | |||||
| Face Normal | |||||
| The normalized vector perpendicular to the plane that a :term:`face` lies in. | |||||
| Each face has its own normal. | |||||
| Geometric Center | |||||
| The mean average of the positions of all vertices making up the object. | |||||
| Gimbal | |||||
| A pivoted support that allows the rotation of an object about a single axis. | |||||
| See also `Gimbal <https://en.wikipedia.org/wiki/Gimbal>`__ on Wikipedia. | |||||
| Gimbal Lock | |||||
| The limitation where axes of rotation can become aligned, | |||||
| losing the ability to rotate on an axis (typically associated with :term:`euler rotation`). | |||||
| - See also `Gimbal lock <https://en.wikipedia.org/wiki/Gimbal_lock>`__ on Wikipedia. | |||||
| - See also `Gimbal lock <https://blender.stackexchange.com/questions/469>`__ on Stackexchange. | |||||
| Global Space | |||||
| See :term:`World Space`. | |||||
| Local Space | |||||
| A 3D coordinate system that originates (for Objects) at the :term:`Object Origin`. | |||||
| or (for Bones) at the :term:`Head` of the :term:`Bone`. | |||||
| Compare to :term:`World Space`. | |||||
| Manifold | |||||
| Manifold meshes, also called *water tight* meshes, | |||||
| define a *closed non-self-intersecting volume* (see also :term:`non-manifold`). | |||||
| A manifold mesh is a mesh in which the structure of the connected | |||||
| faces in a closed volume will always point the normals (and there | |||||
| surfaces) to the outside or to the inside of the mesh without any overlaps. | |||||
| If you recalculate those normals, they will always point at | |||||
| a predictable direction (To the outside or to the inside of the volume). | |||||
| When working with non-closed volumes, a manifold mesh is a mesh in which | |||||
| the normals will always define two different and non-consecutive surfaces. | |||||
| A manifold mesh will always define an even number of non-overlapped surfaces. | |||||
| Mesh | |||||
| Type of object consisting of :term:`vertices <vertex>`, :term:`edges <edge>` and :term:`faces <face>`. | |||||
| Micropolygons | |||||
| A polygon roughly the size of a pixel or smaller. | |||||
| N-gon | |||||
| A :term:`face` that contains more than four :term:`vertices <vertex>`. | |||||
| Non-manifold | |||||
| Non-Manifold meshes essentially define geometry which cannot exist in the real world. | |||||
| This kind of geometry is not suitable for several types of operations, | |||||
| especially those where knowing the volume (inside/outside) of the object is important | |||||
| (refraction, fluids, booleans, or 3D printing, to name a few). | |||||
| A non-manifold mesh is a mesh in which the structure of a | |||||
| non-overlapped surface (based on its connected faces) will not determine | |||||
| the inside or the outside of a volume based on its normals, defining | |||||
| a single surface for both sides, but ended with flipped normals. | |||||
| When working with non-closed volumes, a non-manifold mesh will always | |||||
| determine at least one discontinuity in the normal directions, either | |||||
| by an inversion of a connected loop, or by an odd number of surfaces. | |||||
| A non-manifold mesh will always define an odd number of surfaces. | |||||
| There are several types of non-manifold geometry: | |||||
| - Some borders and holes (edges with only a single connected face), as faces have no thickness. | |||||
| - Edges and vertices not belonging to any face (wire). | |||||
| - Edges connected to three or more faces (interior faces). | |||||
| - Vertices belonging to faces that are not adjoining (e.g. two cones sharing the vertex at the apex). | |||||
| See also: :ref:`Select Non-Manifold <mesh-select-non-manifold>` tool. | |||||
| Normal | |||||
| The normalized vector perpendicular to a surface. | |||||
| Normals can be assigned to vertices, | |||||
| faces and modulated across a surface using :term:`normal mapping`. | |||||
| Object Center | |||||
| Object Origin | |||||
| A reference point used to position, rotate, and scale an :term:`Object` | |||||
| and to define its :term:`Local Space` coordinates. | |||||
| Octahedron | |||||
| An eight-sided figure commonly used to depict the :term:`Bones <Bone>` of an :term:`Armature`. | |||||
| Pivot Point | |||||
| The pivot point is the point in space around which all rotations, | |||||
| scalings and mirror transformations are centered. | |||||
| See also the :doc:`Pivot Point </editors/3dview/object/transform/control/pivot_point/index>` docs. | |||||
| Pole | |||||
| :term:`Vertex` where three, five, or more edges meet. | |||||
| A vertex connected to one, two, or four edges is not a pole. | |||||
| Quad | |||||
| Quadrilateral | |||||
| Quadrangle | |||||
| :term:`Face` that contains exactly four :term:`vertices <vertex>`. | |||||
| Quaternion | |||||
| Quaternion Rotation | |||||
| Rotation method where rotations are defined by four values (X, Y, Z and W). | |||||
| X, Y, and Z also define an :term:`axis`, and W an angle, | |||||
| but it is quite different from :term:`Axis Angle`. | |||||
| Roll | |||||
| Roll Angle | |||||
| The orientation of the local X and Z axes of a :term:`Bone`. | |||||
| Has no effect on the local Y axis as local Y is determined by the location of the :term:`Head` and :term:`Tail`. | |||||
| Smoothing | |||||
| Defines how :term:`faces <face>` are shaded. Face can be either solid (faces are rendered flat) | |||||
| or smooth (faces are smoothed by interpolating the normal on every point of the face). | |||||
| Subdividing | |||||
| Technique for adding more geometry to a mesh. | |||||
| It creates new vertices on subdivided edges, new edges between subdivisions and new faces based on new edges. | |||||
| If new edges cross a new vertex is created at their crossing point. | |||||
| Subsurf | |||||
| Subdivision Surface | |||||
| A method of creating smooth higher poly surfaces which can take a low polygon mesh as input. | |||||
| Sometimes abbreviated to **Subsurf**. | |||||
| See also | |||||
| `Catmull-Clark subdivision surface <https://en.wikipedia.org/wiki/Catmull%E2%80%93Clark_subdivision_surface>`__ | |||||
| on Wikipedia. | |||||
| Tessellation | |||||
| The tiling of a plane using one or more geometric shapes usually resulting in :term:`Micropolygons`. | |||||
| Topology | |||||
| The arrangement of *Vertices*, *Edges*, and *Faces* which define the shape of a mesh. | |||||
| See :term:`vertex`, :term:`edge`, and :term:`face`. | |||||
| Transforms | |||||
| The combined idea of location, rotation and scale. | |||||
| Triangle | |||||
| :term:`Face` with exactly three :term:`vertices <vertex>`. | |||||
| Vertex | |||||
| Vertices | |||||
| A point in 3D space containing a location. It may also have a defined color. | |||||
| Vertices are the terminating points of :term:`edges <edge>`. | |||||
| World Space | |||||
| A 3D coordinate system that originates at a point at the origin of the world. | |||||
| Compare to :term:`Local Space`. | |||||