Introduction

Sage has a wide support for 3D graphics, from basic shapes to implicit and parametric plots.

The following graphics functions are supported:

• plot3d() – plot a 3d function

• parametric_plot3d() – a parametric three-dimensional space curve or surface

• revolution_plot3d() – a plot of a revolved curve

• plot_vector_field3d() – a plot of a 3d vector field

• implicit_plot3d() – a plot of an isosurface of a function

• list_plot3d()- a 3-dimensional plot of a surface defined by a list of points in 3-dimensional space

• list_plot3d_matrix() – a 3-dimensional plot of a surface defined by a matrix defining points in 3-dimensional space

• list_plot3d_array_of_arrays()- A 3-dimensional plot of a surface defined by a list of lists defining points in 3-dimensional space

• list_plot3d_tuples() – a 3-dimensional plot of a surface defined by a list of points in 3-dimensional space

The following classes for basic shapes are supported:

• Box – a box given its three magnitudes

• Cone – a cone, with base in the xy-plane pointing up the z-axis

• Cylinder – a cylinder, with base in the xy-plane pointing up the z-axis

• Line – a 3d line joining a sequence of points

• Sphere – a sphere centered at the origin

• Text – a text label attached to a point in 3d space

• Torus – a 3d torus

• Point – a position in 3d, represented by a sphere of fixed size

The following plotting functions for basic shapes are supported

• ColorCube() – a cube with given size and sides with given colors

• LineSegment() – a line segment, which is drawn as a cylinder from start to end with given radius

• line3d() – a 3d line joining a sequence of points

• arrow3d() – a 3d arrow

• point3d() – a point or list of points in 3d space

• bezier3d() – a 3d bezier path

• frame3d() – a frame in 3d

• frame_labels() – labels for a given frame in 3d

• polygon3d() – draw a polygon in 3d

• polygons3d() – draw the union of several polygons in 3d

• ruler() – draw a ruler in 3d, with major and minor ticks

• ruler_frame() – draw a frame made of 3d rulers, with major and minor ticks

• sphere() – plot of a sphere given center and radius

• text3d() – 3d text

Sage also supports platonic solids with the following functions:

• tetrahedron()

• cube()

• octahedron()

• dodecahedron()

• icosahedron()

Different viewers are supported: a web-based interactive viewer using the Three.js JavaScript library (the default), Jmol, and the Tachyon ray tracer. The viewer is invoked by adding the keyword argument viewer='threejs' (respectively 'jmol' or 'tachyon') to the command show() on any three-dimensional graphic.

• Tachyon – create a scene the can be rendered using the Tachyon ray tracer

• Axis_aligned_box – box with axis-aligned edges with the given min and max coordinates

• Cylinder – an infinite cylinder

• FCylinder – a finite cylinder

• FractalLandscape- axis-aligned fractal landscape

• Light – represents lighting objects

• ParametricPlot – parametric plot routines

• Plane – an infinite plane

• Ring – an annulus of zero thickness

• Sphere- a sphere

• TachyonSmoothTriangle – a triangle along with a normal vector, which is used for smoothing

• TachyonTriangle – basic triangle class

• TachyonTriangleFactory – class to produce triangles of various rendering types

• Texfunc – creates a texture function

• Texture – stores texture information

• tostr() – converts vector information to a space-separated string