Primitive Body Creation

make-plane &key normal point distance [function]

Makes a plane object which is oriented to normal, and passes point. Instead of giving point, distance can be specified.

*xy-plane* [variable]

*yz-plane* [variable]

*zx-plane* [variable]

Figure 10: primitive bodies

make-cube xsize ysize zsize &key name color [function]

makes a cuboid whose sizes in x, y and z directions are xsize, ysize and zsize. The coordinates origin of this cuboid locates at the center of the body.

make-prism bottom-points sweep-vector &key name color [function]

Makes a prism by lifting the shape defined by bottom-points along sweep-vector. If the sweep-vector is a number, not a float-vector, it is taken as the height of the prism in the $z$ direction. Bottom points must be ordered as they define the bottom face of the body. For example, (make-prism '(#f(1 1 0) #f(1 -1 0) #f(-1 -1 0) #f(-1 1 0)) 2.0) makes a cube of height 2.0.

make-cylinder radius height &key (segments 12) name color [function]

Makes a cylinder with specified radius and height. The bottom face is defined on xy-plane and the coordinates origin is located at the center of the bottom face.

make-cone top bottom &key (segments 16) color name [function]

makes a cone body whose summit is the top and bottom face is the bottom. Top is a 3D float-vector. Bottom is either a list of vertices of the bottom face or a radius (scalar). If it is the vertices list, it is order sensitive. + (make-cone #f(0 0 10) (list #f(10 0 0) #f(0 10 0) #f(-10 0 0) #f(0 -10 0)))+ makes a cone of a square bottom.

make-solid-of-revolution points &key (segments 16) name color [function]

Points are revolted along z-axis in the clock wise direction. If two end points in the points list do not lie on z axis, those points make circular faces. Thus, (make-solid-of-revolution '(#f(0 0 1) #f(1 0 0))) makes a cone, and (make-solid-of-revolution '(#f(1 0 1) #f(1 0 0))) makes a cylinder. The points are order-sensitive, and are expected to be arranged from higher $z$ coordinate to lower $z$.

make-torus points &key (segments 16) name color [function]

makes a torus, a donuts like object. Points is a list of vertices on a cross-section.

make-icosahedron &optional (radius 1.0) [function]

Makes a regular body of twenty faces. Each face is a regular triangle.

make-dodecahedron &optional (radius 1.0) [function]

Makes a regular body of twelve faces. Each face is a regular pentagon.

make-gdome abody [function]

By subdividing triangle faces of abody into four subfacets, makes a geodesic dome as a new body. Abody should be an icosahedron initially, and then the result of make-gdome can be given to make-gdome recursively. At each call, the number of faces of the Gdome increases by the factor of four, i.e. 20, 80, 320, 1280, 5120, etc.

(setq g0 (make-icosahedron 1.0))	; 20 facets
(setq g1 (make-gdome g0))		; 80 facets
(setq g2 (make-gdome g1))		; 320 facets
...

grahamhull vertices &optional (normal #f(0 0 1)) [function]

Computes convex-hull for 2D points by Graham's algorithm. Slower than quickhull.

quickhull vertices &optional (normal #f(0 0 1)) [function]

Computes convex-hull for 2D points by the binary search method.

convex-hull-3d vertices [function]

Computes convex-hull for 3D points by gift-wrapping method.

make-body-from-vertices vertices-list [function]

creates a body from lists of vertices each of which define a loop of a face in the consistent order.