The 3D Figure class

This page describes the class used in Codac for 3D visualization.

Figure3D

The basic class for 3D visualization is Figure3D. It is used to generate a .obj file that can be imported in any 3D visualization software.

For online visualization, the free website 3dviewer can be used.

The constructor takes one arguments: the name of the object file.

fig = Figure3D("my_object") # for the object file my_object.obj

Drawing functions

Below are the detailled available drawing functions. The shapes that can be drawn are:

Geometric shapes

  • Box

  • Sphere

  • Arrow

  • Zonotope

  • Parallelepiped

  • Parallelogram

  • Triangle

  • Star-shaped polygon

  • Parametric surface

Vehicles

  • Car

  • Plane

Paving

  • PavingOut (Paving with contractors)

  • PavingInOut (Paving with separators)

  • Subpaving

Note that only the stroke color is used in all of the supported drawing functions.

In addition, a function draw_axes is available to draw the three axes of the 3D space. It can take two arguments :

  • float : the size of the axes

  • Vector : the origin of the axes

Geometric shapes

All the drawable geometric objects can take a last optionnal argument to set up their stroke color. For further details, refer to StyleProperties.

The geometric shapes that can be drawn and their arguments are listed below :

  • draw_box

    • IntervalVector : the box to draw

  • draw_sphere

    • Vector : the center of the sphere

    • Matrix : the scaling matrix

  • draw_arrow

    • Vector : start of the arrow

    • Matrix : orientation of the arrow (first column)

  • draw_zonotope

    • Zonotope: the zonotope to draw

  • draw_parallelepiped

    • Parallelepiped : the parallelepiped to draw

  • draw_parallelogram (defined by \(c + A (p + [-1,1]*v1 + [-1,1]*v2)\))

    • Vector : c, the translation

    • Matrix : A, the scaling

    • Vector : p, base point

    • Vector : v1, first generator

    • Vector : v2, second generator

  • draw_triangle

    • Vector : first point

    • Vector : second point

    • Vector : third point

  • draw_triangle

    • Vector : translation applied to the triangle

    • Matrix : scaling matrix applied to the triangle

    • Vector : first point

    • Vector : second point

    • Vector : third point

The draw_polygon can be used to draw a star-shaped polygon when the vectors are coplanar, and more generally a sequence of adjacent triangles sharing a same vertex.

  • draw_polygon

    • Vector : translation applied to the polygon

    • Matrix : scaling matrix applied to the polygon

    • vector<Vector> : vector where each element is a point of the polygon to draw

  • draw_surface

    • Vector : the translation applied to the surface

    • Matrix : scaling applied to the surface

    • Interval : bounds of p1

    • double : incrementation for p1

    • Interval : bounds of p2

    • double : incrementation for p2

    • function<double, double> -> Vector : the function of the surface, linking each (p1,p2) to a 3D point

Vehicles

All the drawable vehicles can take a last optionnal argument to set up their stroke color. For further details, refer to StyleProperties.

The vehicles that can be drawn and their arguments are listed below :

  • draw_car

    • Vector : center of the car

    • Matrix : orientation of the car

  • draw_plane

    • Vector : center of the plane

    • Matrix : orientation of the plane

    • bool : (optionnal) defines if the yaw axis is up, default to true

Paving

When a paving is drawn, only the inside and boundary boxes are drawn. This is done to avoid outside boxes masking them.

If only one type of paving is drawn (for example a paving with contractors), only one StyleProperties can be defined to choose its edge color. If two types are drawn (boundary and inside), two StyleProperties can be passed to select both colors.

The paving that can be drawn and their arguments are listed below :

  • draw_paving

    • PavingOut | PavingInOut : the paving to draw

  • draw_subpaving

    • Subpaving : the subpaving to draw