Builtin solids with support for textures

Sphere

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

See also: https://en.wikipedia.org/wiki/Sphere

See also: https://mathworld.wolfram.com/Sphere.html

See also: https://mathcurve.com/surfaces.gb/sphere/sphere.shtml

An example in C#

var radius = 1.0;
var numTheta = 20;
var numPhi = 20;
var proc = BuiltIn.SetSphere(radius, numTheta, numPhi);

Left figure: Sphere

Prolate Spheroid

See also: https://mathworld.wolfram.com/ProlateSpheroid.html

See also: https://mathworld.wolfram.com/Spheroid.html

See also: https://en.wikipedia.org/wiki/Spheroid#Prolate_spheroids

See also: https://en.wikipedia.org/wiki/Spheroid#

An example in C#

var radius = 1.0;
var factor1 = 1.5;
var numTheta = 20;
var numPhi = 20;
var proc = BuiltIn.SetProlateSpheroid(radius, factor1, numTheta, numPhi);

\(\quad\)

Left figure: Prolate Spheroid

Right figure: Prolate Spheroid, rotated

Oblate Spheroid

See also: https://mathworld.wolfram.com/OblateSpheroid.html

See also: https://mathworld.wolfram.com/Spheroid.html

See also: https://en.wikipedia.org/wiki/Spheroid#Oblate_spheroids

See also: https://en.wikipedia.org/wiki/Spheroid#

An example in C#

var radius = 1.0;
var factor2 = 0.5;
var numTheta = 20;
var numPhi = 20;
var proc = BuiltIn.SetOblateSpheroid(radius, factor2, numTheta, numPhi);

\(\quad\)

Left figure: Oblate Spheroid

Right figure: Oblate Spheroid, rotated

Ellipsoid

See also: https://mathworld.wolfram.com/Ellipsoid.html

See also: https://en.wikipedia.org/wiki/Ellipsoid

An example in C#

var radius = 1.0;
var factor1 = 1.5;
var factor2 = 0.5;
numTheta = 20;
var numPhi = 20;
var proc = BuiltIn.SetEllipsoid(radius, factor1, factor2, numTheta, numPhi);

\(\quad\)

Left figure: Ellipsoid

Right figure: Ellipsoid, rotated

Torus

A torus is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut.

See also: https://en.wikipedia.org/wiki/Torus

See also: https://mathworld.wolfram.com/Torus.html

See also: https://mathcurve.com/surfaces.gb/tore/tore.shtml

var Radius = 0.6;
var radius = 0.2;
var numTheta = 40;
var numPhi = 40;
var proc = BuiltIn.SetTorus(Radius, radius, numTheta, numPhi);

\(\quad\)

Left figure: Torus

Right figure: 4 Tori

Rectangular cuboid

A rectangular cuboid is a special case of a cuboid with rectangular faces in which all of its dihedral angles are right angles. This shape is also called rectangular parallelepiped or orthogonal parallelepiped.

See also: https://en.wikipedia.org/wiki/Rectangular_cuboid

See also: https://mathworld.wolfram.com/Cuboid.html

An example in C#

var a = 1.0;
var b = 3.0;
var c = 2.0;
var proc = BuiltIn.SetCuboid(a, b, c);

\(\quad\)

Left figure: Rectangular cuboid

Right figure: 4 Rectangular cuboids

Rhombohedron

A rhombohedron is a parallelepiped bounded by six rhombi such that opposite faces are congruent. Special cases include the cube, acute golden rhombohedron, and obtuse golden rhombohedron.

See also: https://en.wikipedia.org/wiki/Rhombohedron

See also: https://mathworld.wolfram.com/Rhombohedron.html

See also: https://mathworld.wolfram.com/GoldenRhombohedron.html

See also: https://mathworld.wolfram.com/AcuteGoldenRhombohedron.html

See also: https://mathworld.wolfram.com/ObtuseGoldenRhombohedron.html

An example in C#

var theta = 60.0;
var proc = BuiltIn.SetRhombohedron(theta);

\(\quad\)

Left figure: Rhombohedron

Right figure: Rhombohedron, tilted

Parallelepiped

A rectangular cuboid is a special case of a cuboid with rectangular faces in which all of its dihedral angles are right angles. This shape is also called rectangular parallelepiped or orthogonal parallelepiped.

See also: https://en.wikipedia.org/wiki/Parallelepiped

See also: https://mathworld.wolfram.com/Parallelepiped.html

An example in C#

var a = 1.0;
var b = 3.0;
var c = 2.0;
var alpha = 90.0;
var beta = 90.0;

var proc = BuiltIn.SetParallelepiped(a, b, c, alpha, beta);

\(\quad\)

Left figure: Parallelepiped

Right figure: Parallelepiped, tilted