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Shapes

Shapes are the elements that interact with light, building the scene. Everything, from sky to ground to other objects are shapes, that have been eventually transformed and combined to give rise to images. There are some basic shapes available, and more complex can be obtained by CSG constructions.

Basic

Sphere

Sphere is by default the canonical one, with radius=1 and the center in the origin of the axes. Any deformation must be set with a scaling transformation.
The only two parameters are the material and the transformation.

...
sphere ( sky, scaling([20.0, 20.0, 20.0]) )
...

Plane

The plane by default is the xy plane with z=0. Just like the sphere it accepts a material and a transformation parameter.

...
plane ( ground, scaling([20.0, 20.0, 20.0]) )
...

Cylinder

Default cylinders are the one with unit radius and unit height, from z=-0.5 to z=0.5. As for the previous shapes they accept a material and a transformation.

...
cylinder ( woodMat, translation([2.0, 0.0, 1.0]) )
...

Box

Boxes are a little more complicated. Their dimension are given by the point of minimal value of vertices' coordinates and the maximum one (which are the 2 opposite vertices along one specific diagonal), even though a scaling transformation is always possible. Then the usual material and transformation parameter are accepted.

box (           
    (-0.5, -0.5, -0.5), #Min point
    (0.5, 0.5, 0.5),    #Max point
    minecraft,
    identity
)

Hyperboloid

Hyperboloids are shapes defined by the quadratic equation: x2 + y2 - z2 = 1.
The fragment of hyperboloid to be considered, is defined giving the minimum and the maximum values of z accepted. Then the usual material and transformation parameter are accepted.

hyperboloid (           
    -0.5,   #Min Z
    0.5,    #Max Z
    marble,
    identity
)

CSG

Of course the infinite complexity of shapes cannot be captured by only basic shapes. Constructive Solid Geometry (CSG), does not provide a definitive answer to this problem, but offers a powerful tool for combining different basic shapes together, that can be exploited to reach exceptional results.
The combination of shapes is based on three logical operations:

Remember that shape definitions can be of great help when trying to build a complex CSG object, we recommend to give a look to its documentation in the input file section.

Difference

Difference is the operation that, given 2 shapes, builds the object where all the point belonging to the first shape and not to the second are considered.
In the following example from a box, two other boxes are removed, each with a different rotation, giving birth to a triangular shape.

shape baseBox box (
    (-0.05, 0.0 , 0.0),
    (0.05, 1.0 , 1.0),
    marble,
    identity
)

shape cutBox box (
    (-1.0, -3.0 , 0.0),
    (1.0, 3.0 , 1.0),
    marble,
    identity
)

shape baseCrossUnit difference(
    baseBox(identity),
    cutBox(rotation_x(63),
    identity
)

shape crossUnit difference (
    baseCrossUnit(identity),
    cutBox( translation([0, 1.0, 0]) * rotation_x(-63) ),
    translation([0, -0.5, -0.5)
)

crossUnit(identity)
With the difference it is possible to obtain a triangular shape, which will be useful for the top of the final figure

Union

Union is the operation that combines two shapes into an object resulting from taking all the points of both shapes. It is useful to build together shapes into a unique structure, as in the example.

shape base cylinder (
    marble,
    scaling([1.15, 1.15, 0.2]) * translation([0, 0, 0.5])
)

shape base2 union (
    base,
    base ( scaling([0.85, 0.85, 1.5]) * translation([0, 0, 0.2]) )
)

shape body union (
    base2,
    hyperboloid (
        0.5, 
        0.5,
        marble,
        translation([0, 0, 2.0]) * scaling([0.55, 0.55, 3.0])
)

body (identity)
With the union some cylinders and an hyperboloid can be built up together

Intersection

Intersection is the last CSG operation available, and builds the object considering all the points that belong to both the shapes. For example, intersecting a Cylinder and a Sphere will result in: 

intersection(
    sphere( marble, scaling([3.0, 3.0, 3.0]) ),
    cylinder( marble, translation([0, 0, 2.9]) * scaling([0.5, 0.5, 0.2]) ),
    identity
)
Intersection is what we need for the top of our figure

And here is the result of a complex CSG object, build up of several combinations, and available in KTracer as a variable of name KTKing.

The King of a chess set, with marble procedural texture

Advanced CSG

Some fascinating shapes have been made available to programmers for their images:

  • KTArmchair A nice armchair for your living room
  • KTKing The most important piece in the chess board

If you have some interesting creations, let us know via issues or via e-mail. If you like to share it with the community, we will provide to extend the available shapes.

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