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| − | = Arbitrary convex polyhedra = | + | =Arbs= |
| | + | Objects with an arbitrary number of points and flat faces... |
| | + | ==arb8== |
| | + | Arbitrary straight-edged shape with 8 vertices. |
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| − | An '''arbitrary convex polyhedron''' ('''arb''') is a geometric volume that is completely enclosed by a set of 3-dimensional planes. Each has a set of straight-edged, flat '''faces''' outlined by the intersections of those planes. The intersection of each pair of planes is a line whose intersections with other planes defines a pair of '''vertices'''. The line segment between those two vertices is an '''edge''' of the polyhedron that is shared by two faces. Each vertex is common to an equal number (at least three) of faces and edges.
| + | ;Handled by: make in form create |
| | + | ;Arguments: 8 Vertices in the following order: 1234 vertices for the front face, starting at bottom left, counterclockwise; then 5678 vertices for the rear face, starting at bottom left, counterclockwise. |
| | + | ;Example: |
| | + | in unitcube.s arb8 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 |
| | + | creates the unit cube (first vertex at the origin, extends for 1 unit in x, y and z direction). |
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| − | For example, a rectangular parallelepiped is enclosed by three orthogonal pairs of parallel planes. Their intersections define six faces, each with four edges and four vertices. There are a total of 12 edges (each shared by two faces) and 8 vertices (each shared by three faces and three edges).
| + | == arb7 == |
| | + | Special case of arb8, except with point 8 merged into point 5, making the left face triangular |
| | + | ;Handled by: make in form(arb8) create |
| | + | == arb6 == |
| | + | Arbitrary straight-edged shape with 6 vertices, special case of arb8. |
| | + | ;Handled by: make in form(arb8) create |
| | + | ;Arguments: 6 Vertices in the following order: 1234 vertices for the front face, starting at bottom left, counterclockwise; then back edge is 5 on bottom, 6 on top. Top and bottom faces are triangles. |
| | + | ;Example: |
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| − | The BRL-CAD geometry file format defines two types of records for such polyhedra:
| + | in arb6.s arb6 1 -1 -1 1 1 -1 1 1 1 1 -1 1 -1 0 -1 -1 0 1 |
| − | * [[#ARB8 Records|'''arb8'''s]] are specified by a set of eight vertices.
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| − | * [[#ARBN Records|'''arbn'''s]] are specified by a set of intersecting planes, each defined by four coefficients.
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| − | Although any polyhedron can be defined and stored as an arbn, the arb8 record type is more commonly employed because it is simpler to work with and still accommodates most constructive solid geometry applications.
| + | == arb5 == |
| | + | special case of arb8. |
| | + | ;Handled by: make in form(arb8) create |
| | + | == arb4 == |
| | + | special case of arb8. |
| | + | ;Handled by: make in form(arb8) create |
| | + | == arbn == |
| | + | Arbitrary solid bounded by N planes. |
| | + | ;The solid is constructed by N sets of plane coefficients and distance magnitudes, that define space which is ~outside~ the solid. The coefficients define a vector whose normal is a plane parallel to the face of the solid. The surface of the solid is at the perscribed distance along this vector. |
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| − | == ARB8 Records ==
| + | The distances may be negative and are used when a face lies on the opposite side of the origin as the tip of its vector. An example is if the left side of a box lies on the positive X axis. In this case, because the left side is being defined, the vector points left (coefficients -1 0 0), but since the point is on the positive X axis its distance is opposite its vector and therefore negative. |
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| − | An '''arb8''' record is specified by a set of eight {X, Y, Z} vertices designated V1 through V8, which need not all be unique. BRL-CAD uses such records to represent polyhedra having four, five or six faces:
| + | ;Handled by: make in create |
| | + | ;Arguments |
| | + | :Number of planes |
| | + | :xyz direction vector and distance for each plane |
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| − | * '''arb8''' shapes have eight unique vertices. They represent '''hexahedra''' that have six quadrilateral faces sharing eight edges. In addition to simply specifying the {X, Y, Z} coordinates of those vertices, MGED provides easier ways to create the following specific types of hexahedra:
| + | ;Example |
| − | ** '''3ptarb''' shapes represent '''right quadrilateral prisms''', which are extruded quadrilaterals having parallel ends connected by four rectangular sides.
| + | :in arbn.s arbn 8 1 0 1 1 -1 0 0 1 0 1 0 1 0 -1 0 1 0 0 1 1 0 0 -1 1 0.5 0.5 0.5 1 -0.5 -0.5 -0.5 1 |
| − | ** '''box''' shapes represent '''parallelepipeds''', whose faces comprise three pairs of equal parallelograms. Unlike a common box, those faces need not be rectangular—if they are, the enclosed volume is a rectangular parallelepiped.
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| − | ** '''rpp''' shapes represent '''rectangular parallelepipeds''' (also known as '''cuboids''' and '''rectangular prisms'''), whose faces comprise three pairs of equal rectangles. If one pair of faces are squares, the volume is a '''square prism'''. If all of them are squares, the volume is a '''cube''' (geometrically, there cannot be just two pairs of square faces).
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| − | * '''arb7''' shapes have seven unique vertices. They represent hexahedra that have four quadrilateral and two triangular faces sharing eleven edges. They can only be created by specifying the {X, Y, Z} coordinates of those vertices.
| + | ;Example with negative distance |
| | + | :in arbn2.s arbn 6 1 0 0 100 -1 0 0 -10 0 1 0 200 0 -1 0 -10 0 0 -1 0 0 0 1 1.5 |
| | + | :...is equivalent to... |
| | + | :in rpp.s rpp 10 100 10 200 0 1.5 |
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| − | * '''arb6''' shapes have six unique vertices. They represent '''triangular prisms''' and '''truncated tetrahedra''', which are '''pentahedra''' that have two triangular ends connected by three quadrilateral sides sharing nine edges. In addition to simply specifying the {X, Y, Z} coordinates of their vertices, MGED provides an easier way to create one specific type of hexahedron:
| + | ==box== |
| − | ** '''raw''' ('''right angle wedge''') shapes are '''triangular prisms''' whose ends are parallel to each other. Interestingly enough, they don't seem to require any right angles. If the ends are perpendicular to the connecting edges, the shape is a '''right triangular prism''' and has rectangular sides. Presumably two of the rectangular sides of an actual right-angle wedge would also be perpendicular to each other.
| + | Special case of arb8 |
| | + | ;Handled by: in form(arb8) |
| | + | ;Arguments: Vertex of first corner, direction vectors for height, width, and depth |
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| − | * '''arb5''' shapes have five unique vertices. They represent '''quadrahedra''', which are pentahedra that have a quadrilateral base and four triangular sides sharing eight edges. If such a volume has a rectangular base it is a '''rectangular pyramid''', one with a square base is a '''square pyramid'''.
| + | ==raw== |
| | + | Right Angle Wedge, special case of arb6 |
| | + | ;Handled by: in form(arb8) |
| | + | ;Arguments: Vertex of first corner, direction vectors for height, width, and depth |
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| − | * '''arb4''' shapes have four unique vertices. They represent '''tetrahedra''', which have four triangular faces sharing six edges. If all four triangles are equilateral, the shape is a '''regular tetrahedron'''.
| + | ==rpp== |
| − | | + | Rectangular Parallelpiped, special case of arb8 |
| − | == ARBN Records == | + | ;Handled by: make in form(arb8) create |
| − | | + | ;Arguments: xmin xmax ymin ymax zmin zmax |
| − | An '''arbn''' record is specified by N sets of intersecting planes, each defined by four coefficients:
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| − | * the {X, Y, Z} coefficients of the plane's normal vector pointing outward from the center of the arbn shape, and
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| − | * the perpendicular distance of that plane from the origin.
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| − | As discussed in the [[Creating and editing arbn primitives]] article, BRL-CAD uses such primitives to represent polyhedra having any number of sides, edges and vertices.
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| | =Ellipsoids= | | =Ellipsoids= |
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| − | ==brep== | + | ==nurb== |
| − | [[NURBS|see NURBS]]
| + | Non-uniform rational b-spline |
| | + | ;Handled by: none? |
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| | ==spline== | | ==spline== |
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| | ;Handled by: make form(sketch editor) create | | ;Handled by: make form(sketch editor) create |
| | ;See also: [[sketch]] | | ;See also: [[sketch]] |
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| − | ==annot==
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| − | 2D annotation primitive
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| − | ;Handled by: in command
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| − | See: [[annot]]
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| | ==grip == | | ==grip == |
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| | ;Arguments: minor type (fdcsiLCSIL), data file, number of values | | ;Arguments: minor type (fdcsiLCSIL), data file, number of values |
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| − | == submodel ==
| + | [[Determining the properties of primitives]] |
| − | Instanced Submodel
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| − | :Handled by: in make form create
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| − | :Arguments:
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| − | ;file: File holding the referenced geometry. 0-length if geometry is in the same file.
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| − | ;treetop: Single name for the geometry to reference.
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| − | A submodel is a reference to another geometry, possibly in a separate file.
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