Cython branch: How to Add New Optics

When working with the cython raypier branch, be sure you have the latest Cython version installed (as of writing, v0.12.1 was the latest).

Creating a new Face

Subclasses of raypier.core.ctracer.Face perform the mechanics of the ray-tracing operation. Most existing subclasses are defined in cfaces.pyx. To define a new face object, two “C” methods need to be defined:

cdef double intersect_c(vector_t p1, vector_t p2)

Computes the intersection of a ray with the surface, where p1 and p2 are two points defining the start and end points of an incoming ray, in the local coordinate system. The method returns a single floating-point value representing the distance along the ray where an intersection occurs. If no intersection is found, a value <= 0 may be returned (I tend to return zero, if no intersection occurs).

cdef vector_t compute_normal_c(vector_t p)

Computes the outward normal vector for the surface at the given point, p. These are also defined w.r.t. the local coordinate system.

Note, these two methods are ‘cdef-methods’ and hence not callable directly from python. Be sure to type all the variables you use, to be sure of good performance. Face objects also have python-callable methods compute_normal() and intersect(). These call the cdef methods internally. Don’t bother trying to overload these from python as it won’t work (and even if it did, performance would be horrible).

The vector_t structure is used to represent 3D points (i.e. it’s a 3d vector), and has .x and .y and .z members. Outside the comfort of python/numpy, vector algebra is significantly less pleasant. The ctracer module defines a number of inline functions to (partially) simplify working with vector_t’s. For vector arithmatic, you can use:

  • addvv_(vector_t a, vector_t b) #add two vectors

  • addvs_(vector_t a, double b) #adds a vector and a scalar

  • multvv_(vector_t a, vector_t b) #multiplies two vectors

  • multvs_(vector_t a, double b) #multiplies a vector and a scalar


Similar function are defined for subtraction and element-wise division. The ‘vv’ function denote operations on two vectors, ‘vs’ denotes operations on a vector and a scalar. The trailing underscore is a convention I’m adopting to indicate that the method is a ‘C’-method (i.e. not python callable).

Some of the other utility functions are:

cdef inline vector_t set_v(vector_t v, object O)

Takes a vector v and an 3-sequence O. Copies the values from the sequence into the vector and returns it (why does it need the v argument, though?).

cdef inline double sep_(vector_t p1, vector_t p2)

Computed the linear separation between two points

cdef inline double dotprod_(vector_t a, vector_t b)

Calculates the dot-product of the given vectors

cdef inline vector_t cross_(vector_t a, vector_t b)

Calculates the vector-product of it’s arguments

cdef inline vector_t norm_(vector_t a)

Computes the normalised vector from its input (i.e. scales it’s input to unit magnitude).

cdef inline double mag_(vector_t a)

Calculates the magnitude of it’s input

cdef inline double mag_sq_(vector_t a)

Calculates the square of the magnitude of it’s input

cdef inline vector_t invert_(vector_t v)

Inverts it’s input

Most of the cdef functions and cdef-methods have companion def functions/methods which are callable from python and wrap the associated cdef operation. These are mostly used in testing. The python-callable versions incure the normal python interpreter overhead, and hence are not directly useful in the fast C-level tracing process.

The intersect_c and compute_normal_c cdef methods are all you need to make a new face. Obviously, you can add additional methods / attributes to implement the functionality required.

You can optionally give your custom Face class a params attribute (define it as a class-attribute) which should contain a list of attribute names which should be synchronised from the face owner to the face when a tracing operation is initiated.

Creating a new Traceable

Traceables (i.e. subclasses of raypier.bases.Traceable) are the basic unit of an optical model. Most of the functionality in the Traceable subclasses is to implement their VTK visual representation. The ray-tracing operation is handled by Face objects. Traceables own an instance of a ctracer.FaceList which turn has a list of Face objects (I choose FaceList has a list of faces, rather than FaceList is a list of faces, as it was simpler to implement). The FaceList contains the coordinate transform which maps betwee global coords and the local coords of the Traceable. Thus, all Faces belonging to a Traceable share a common transform.

To create a new Traceable, you subclass Traceable or some other more suitable subclass (transmitting optical components can derive from raypier.bases.Optic, which provides a complex refractive index). You should define a new _faces_default method which creates the FaceList for that object and populates it with the Faces appropriate to the object. Simple synchronisation between the Traceable and the Faces can be handled using the params Face class attribute described above. In most cases, more sophisticated synchronisation is required and can be handled using trait-notifications for all traits on which the Faces depends.

The physics of ray-scattering (i.e. the generation of new rays at the point of intersection) is handled by ctracer.InterfaceMaterial objects. InterfaceMaterial is an abstract base class. There are two concrete subclasses defined in the ctracer module: PECMaterial and DielectricMaterial. The former represents a perfect metal reflector. The later is a normal dielectric surface. Typically, an Optic (or Traceable subclass) will have an InterfaceMaterial trait. This will be passed to it’s faces in the _faces_default method (so all faces share the same InterfaceMaterial). However, this is not a requirement: faces can have independent materials, or share them.

Custom Interface Materials

InterfaceMaterial subclasses provide a cdef method:

cdef eval_child_ray_c(self, ray_t *old_ray,
                          unsigned int ray_idx,
                          vector_t point, vector_t normal,
                          RayCollection new_rays)

This is called for each ray intersection to create a new ray. The arguments are as follows:

old_Ray - a pointer to the incoming ray_t structure ray_idx - the index of the incoming ray in it’s RayCollection array point - the position, in global coords, of the intersection normal - the normal vector of the surface, at the point of intersection new_rays - the target RayCollection for new rays

This method should call new_rays.add_new_ray() to create as many new rays as necessary. Thus, multiple ray generation can occur at an intersection (as might be found for a diffracting interface material).

Cython Tips and Tricks

If you find performance is less than you expected, try running “cython -a yourfile.pyx” (replace yourfile.pyx with whatever .pyx file you’re analysing, cfaces.pyx maybe). This produces a html-version of your file, with highlighting to show where the python API is being invoced. The less yellow the better (and red-highlights indicate real performance bottlenecks). This is a very cool feature of Cython.

Avoid cpdefs (i.e. methods with automatically created python wrappers), as extra overhead is incured to check for python overloading.

Creating and destroying python objects is expensive (it invokes the garbage collector / changes ref-counts etc.). However, read-only access to items in lists is fast.

Surprisingly, I can find no speed benefit in passing parameters by reference, compared to passing by values (for fixed-size types, at least).