Small Blender Things

Raytracing concepts and code, part 6, specular reflection for lights

This is an article in a multipart series on the concepts of ray tracing. I am not sure where this will lead but I am open to suggestions. We will be creating code that will run inside Blender. Blender has ray tracing renderers of course but that is not the point: by reusing Python libraries and Blender's scene building capabilities we can concentrate on true ray tracing issues like shader models, lighting, etc.
I generally present stuff in a back-to-front manner: first an article with some (well commented) code and images of the results, then one or more articles discussing the concepts. The idea is that this encourages you to experiment and have a look at the code yourself before being introduced to theory. How well this works out we will see :-)

So far the series consists of the several articles labeled ray tracing concepts

Until now the reflections have been a bit dull because our shader model only takes into account the diffuse reflectance, so lets take a look at how we can add specular reflectance to our shader.
The effect we want to achieve is illustrated in the two images below where the green sphere on the right had some specular reflectance. Because of this it shows highlights for the two points lamps that are present in the scene.

The icosphere shows faceting because we did not yet anything to implement smooth shading (i.e. interpolating the normals across a face) but with added some smooth subdivisions to show off the high lights a bit better.
In the image below we see that we also look at the hardness of the specular reflections in our shader model, with a high value of 400 giving much tighter highlights than the default hardness of 50.

In both images the red cube has no specular intensity and the blue one has a specular intensity of .15 and a hardness of 50.

Specular color, specular intensity and hardness are properties of a material so we have also exposed the relevant panel to our custom renderer so that the user can set these values.

Code

The code changes needed in the inner shading loop of our ray tracer are limited:

if hit:
 diffuse_color = Vector((0.8, 0.8, 0.8))
 specular_color = Vector((0.2, 0.2, 0.2))
 mat_slots = ob.material_slots
 hardness = 0
 if len(mat_slots):
  diffuse_color = mat_slots[0].material.diffuse_color \
                    * mat_slots[0].material.diffuse_intensity
  specular_color = mat_slots[0].material.specular_color \
                    * mat_slots[0].material.specular_intensity
  hardness = mat_slots[0].material.specular_hardness

  ... identical code left out ...
  
  if not lhit:
   illumination = light * normal.dot(light_dir)/light_dist
   color += np.array(diffuse_color) * illumination
   if hardness > 0:  # phong reflection model
    half = (light_dir - dir).normalized()
    reflection = light * half.dot(normal) ** hardness
    color += np.array(specular_color) * reflection

We set reasonable defaults (line 2 - 5), override those defaults if we have a material on this object (line 6 - 11) and then, if we are not in the shadow, calculate the diffuse component of the lighting as before (line 16 - 17) and the finally add a specular component (line 18 - 21)

For the specular component we use the Phong model (or actually the Blinn-Phong model). This means we look at the angle between the normal (shown in light blue in the image below) and the half way vector (in dark blue). The smaller the angle the tighter the highlight. The tightness is controlled by the hardness: we raise the cosine of the angle (which is what the dot product is that we compute in line 20) to the power of this hardness. Note that the half way vector is the normalized vector that points exactly in between the direction of the light and the camera as seen from the point being shaded. That is why we have a minus sign rather than a plus sign in line 19 because dir in our code points from the camera towards the point being shaded.

Code availability

The code is available on GitHub.

Raytracing concepts and code, part 5, diffuse color

Our rendered scene so far mainly consists of fifty shades of gray and that might be exciting enough for some but it would be better if we could spice it up with some color.

For this we will use the diffuse color of the first material slot of an object (if any). The code so far needs very little change to make this happen:

            # the default background is black for now
            color = np.zeros(3)
            if hit:
                # the get the diffuse color of the object we hit
                diffuse_color = Vector((0.8, 0.8, 0.8))
                mat_slots = ob.material_slots
                if len(mat_slots):
                    diffuse_color = mat_slots[0].material.diffuse_color
                        
                color = np.zeros(3)
                light = np.ones(3) * intensity  # light color is white
                for lamp in lamps:
                    # for every lamp determine the direction and distance
                    light_vec = lamp.location - loc
                    light_dist = light_vec.length_squared
                    light_dir = light_vec.normalized()
                    
                    # cast a ray in the direction of the light starting
                    # at the original hit location
                    lhit, lloc, lnormal, lindex, lob, lmat = scene.ray_cast(loc+light_dir*eps, light_dir)
                    
                    # if we hit something we are in the shadow of the light
                    if not lhit:
                        # otherwise we add the distance attenuated intensity
                        # we calculate diffuse reflectance with a pure 
                        # lambertian model
                        # https://en.wikipedia.org/wiki/Lambertian_reflectance
                        color += diffuse_color * intensity * normal.dot(light_dir)/light_dist
            buf[y,x,0:3] = color

In lines 5-8 we check if there is at least one material slot on the object we hit and get its diffuse color. If there is no associated material we keep a default light grey color.
This diffuse color is what we use in line 28 if we are not in the shadow.

Code availability

The code is available on GitHub.

Raytracing: concepts and code, part 4, the active camera

In a further bit of code cleanup we'd like to get rid of the hardcoded camera position and look at direction by using the location of the active camera in the scene together with its rotation.
Fortunately very little code has to change to make this happen in our render method:

    # the location and orientation of the active camera
    origin = scene.camera.location
    rotation = scene.camera.rotation_euler

Using the rotation we can first create the camera ray as if it originated in the default -Z direction and then simply rotate it using the camera location:

    aspectratio = height/width
    # loop over all pixels once (no multisampling)
    for y in range(height):
        yscreen = ((y-(height/2))/height) * aspectratio
        for x in range(width):
            xscreen = (x-(width/2))/width
            # align the look_at direction
            dir = Vector((xscreen, yscreen, -1))
            dir.rotate(rotation)

Later we might even adapt this code to take into account the field of vision, but for now at least we can position and aim the active camera in the scene any way we like.

Code availability

The code is available on GitHub.

Raytracing: concepts and code, part 3, a render engine

The code presented in the first article of this series was a bit of a hack: running from the text editor and lots of built-in assumptions is not the way to go so lets refactor this in a proper render engine that will be available alongside Blender's built-in renderers:

A RenderEngine

All we really have to do is to derive a class from Blender's RenderEngine class and register it.The class should provide a single method render() that takes a Scene parameter and returns a buffer with RGBA pixel values.

class CustomRenderEngine(bpy.types.RenderEngine):
    bl_idname = "ray_tracer"
    bl_label = "Ray Tracing Concepts Renderer"
    bl_use_preview = True

    def render(self, scene):
        scale = scene.render.resolution_percentage / 100.0
        self.size_x = int(scene.render.resolution_x * scale)
        self.size_y = int(scene.render.resolution_y * scale)

        if self.is_preview:  # we might differentiate later
            pass             # for now ignore completely
        else:
            self.render_scene(scene)

    def render_scene(self, scene):
        buf = ray_trace(scene, self.size_x, self.size_y)
        buf.shape = -1,4

        # Here we write the pixel values to the RenderResult
        result = self.begin_result(0, 0, self.size_x, self.size_y)
        layer = result.layers[0].passes["Combined"]
        layer.rect = buf.tolist()
        self.end_result(result)

Option panels

For a custom render engine all panels in the render and material options will be hidden by default. This makes sense because not all render engines use the same options. We are interested in just the dimensions of the image we have to render and the diffuse color of any material so we explicitly add our render engine to the list of COMPAT_ENGINES in each of those panels, along with the basic render buttons and material slot list.

def register():
    bpy.utils.register_module(__name__)
    from bl_ui import (
            properties_render,
            properties_material,
            )
    properties_render.RENDER_PT_render.COMPAT_ENGINES.add(CustomRenderEngine.bl_idname)
    properties_render.RENDER_PT_dimensions.COMPAT_ENGINES.add(CustomRenderEngine.bl_idname)
    properties_material.MATERIAL_PT_context_material.COMPAT_ENGINES.add(CustomRenderEngine.bl_idname)
    properties_material.MATERIAL_PT_diffuse.COMPAT_ENGINES.add(CustomRenderEngine.bl_idname)

def unregister():
    bpy.utils.unregister_module(__name__)
    from bl_ui import (
            properties_render,
            properties_material,
            )
    properties_render.RENDER_PT_render.COMPAT_ENGINES.remove(CustomRenderEngine.bl_idname)
    properties_render.RENDER_PT_dimensions.COMPAT_ENGINES.remove(CustomRenderEngine.bl_idname)
    properties_material.MATERIAL_PT_context_material.COMPAT_ENGINES.remove(CustomRenderEngine.bl_idname)
    properties_material.MATERIAL_PT_diffuse.COMPAT_ENGINES.remove(CustomRenderEngine.bl_idname)

reusing the ray tracing code

Our previous ray tracing code is adapted to use the height and width arguments instead of arbitrary constants:

def ray_trace(scene, width, height):     

    lamps = [ob for ob in scene.objects if ob.type == 'LAMP']

    intensity = 10  # intensity for all lamps
    eps = 1e-5      # small offset to prevent self intersection for secondary rays

    # create a buffer to store the calculated intensities
    buf = np.ones(width*height*4)
    buf.shape = height,width,4

    # the location of our virtual camera (we do NOT use any camera that might be present)
    origin = (8,0,0)

    aspectratio = height/width
    # loop over all pixels once (no multisampling)
    for y in range(height):
        yscreen = ((y-(height/2))/height) * aspectratio
        for x in range(width):
            xscreen = (x-(width/2))/width
            # get the direction. camera points in -x direction, FOV = approx asin(1/8) = 7 degrees
            dir = (-1, xscreen, yscreen)
            
            # cast a ray into the scene
            
            ... indentical code omitted ...

    return buf

Code availability

The code is available on GitHub. Remember that any test scene should be visible from an virtual camera located at (8,0,0) pointing in the -x direction. The actual camera is ignored for now.

Raytracing: concepts and code, part 2, from rays to pixels

In the first article I presented some code to implement a very basic raytracer. I chose Blender as a platform for several reasons: it has everything to create a scene with objects so we don't have to mess with implementing geometry and the functions to calculate intersections ourselves. It also provides us with the Image class that lets us store the image that we create pixel by pixel when raytracing. Finally it also comes with powerful libraries of math and vector functions, saving us the drudgery of implementing this ourselves. All of this allows us to focus on the raytracing proper.

What is ray tracing?

When ray tracing we divide the image we are creating into pixels and shoot a ray from a point in front of this image (the camera location) into the scene. The first step is then to determine whether this ray hits any object in the scene. If not we give our pixel the background color but if we do hit an object we color this picture with a different color that is dependent on the material properties of the object and any light that reaches that point.

So if we have calculated the location where our first ray (or camera ray, red in the illustration) hits the closest bit of geometry, the next step is to determine how much light reaches that point and combine this with the material information of the object.

There are many ways to approach this and in our first implementation we cast rays from this point in the direction of any lamp in the scene. These rays are often called shadow rays (green in the illustration) because if we hit something that means that an object blocks the light from this lamp and that the point we are shading lies in the shadow of the lamp. If we are not in the shadow we can calculate the light intensity due to this lamp by taking its original intensity and dividing it by the squared distance between our point and the lamp.

Once we have calculated the intensity we can use it to determine the diffuse reflectance. Diffuse reflectance causes light to be scattered in all directions. The exact behavior will be determined by the microstructure of the surface and there are different models to approximate this.

To start we will use the so called Lambert model. In a nutshell this model assumes that incident light is uniformly scattered in all directions which means that if a surface is facing a light it will look bright and this brightness will diminish if the direction of the surface normal diverges from this direction. The brightness we observe is therefore not dependant on the camera orientation but just on the local orientation of the geometry. Different models exist that take into account roughness and anisotropy but that is something for later.

Review: CinemaColour For Blender

Recently I was offered a change to look at CinemaColour For Blender by FishCake.

CinemaColour offers a large collection of professional color management looks (LUTs) to use with Blender's built-in Filmic color management. Check out the artist's website for some great examples. It comes in the form of an add-on that installs over a hundred looks and also offers a convenient way to browse and select the looks that are available. In this short article I'll have a good look at my experiences with the add-on and the looks it offers.

Filmic color management

Since well over a year Blender has incorporated Roy Sobotka's Filmic color management solution and everybody, really everybody, has been very enthusiastic about it ever since. This enthusiasm is well deserved because when using Filmic your renders may almost immediately gain a lot of realism, mainly by mapping the wide range of light intensities in your scene to the limited range of intensities your monitor can handle in a much better way than before. No more blown out highlights or loss in details in the deep shadows!

Looks

Filmic uses lookup tables (LUTs) to convert these intensities and by selecting different look up tables you can create different looks: not only can you choose these looks to present you with more or less contrast in your renders but because these lookups are done independently for all color channels you can use looks that add a color tone to your render. These tones can greatly influence the feel of your scene and because this mapping is done after the result is rendered and composited, it is very easy to experiment with the overall look.

CinemaColour for Blender

Now creating professional looks and making them available for use in Blender is a real craft and that is where CinemaColour comes in. The add-on installs over a hundred different looks and panel in the Scene options where you can easily browse through the list of choices and apply them to your scene. The available looks are grouped in several collections and each look has a name that hints at major blockbuster films that feature a similar look. The available looks range from subtle contrasts to moody color settings and everything in between. Some examples are shown below:

Look: CS ST Y L 3

Look: B2 Gangster

Look: B2 Sniper Alt

Look: B2 The Phantom Alt

Look: B2 Wade Pool

Look: CC Crush

Look: CM Ice

Note that we did not have to render our scene again to generate these looks, so generating these examples after render the scene a single time only took seconds.

Conclusion

A great set of professional looks done by someone who clearly knows their color management. The selection of the provided looks is also intuitive and every artist that is serious about the overall look and feel of their renders should check this out. CinemaColour is available on BlenderMarket.

Raytracing: concepts and code, part 1, first code steps

In this article I will show how to implement a minimal raytracer inside Blender. Of course Blender has its own very capable renderers, like Cycles, but point is to illustrate some ray tracing concepts without being bogged down with tons of code that have nothing to do with ray tracing per se.

By using Blender's built-in data structures like a Scene and an Image and built-in methods like ray_cast() we don't have to implement difficult algorithms and data structure like ray/mesh intersection and BVH-trees for example, but we can concentrate on things like primary and secondary rays, shadows, shading models etc. etc.

The scene

The scene we will be working with at first looks like this:

Nothing more than a plane, a couple of cubes and an icosphere. Plus two point lights to illuminate the scene (not visible in this screenshot).

In rendermode the scene looks like this:

Note that we didn't assign any materials so everything is shaded with a default shader.

Our result

Now the result of the minimal raytracer shown in the next section looks like this:

There are clear differences of course, and we'll work on them in the future, but the general idea is similar: light areas close to lights and visible shadows. How many lines of code do you think is needed for this?

The code

The code to implement this is surprisingly compact (and more than half of it is comments):

import bpy
import numpy as np

scene = bpy.context.scene

lamps = [ob for ob in scene.objects if ob.type == 'LAMP']

intensity = 10  # intensity for all lamps
eps = 1e-5      # small offset to prevent self intersection for secondary rays

# this image must be created already and be 1024x1024 RGBA
output = bpy.data.images['Test']

# create a buffer to store the calculated intensities
buf = np.ones(1024*1024*4)
buf.shape = 1024,1024,4

# the location of our virtual camera
# (we do NOT use any camera that might be present)
origin = (8,0,0)

# loop over all pixels once (no multisampling)
for y in range(1024):
    for x in range(1024):
        # get the direction.
        # camera points in -x direction, FOV = 90 degrees
        dir = (-1, (x-512)/1024, (y-512)/1024)
        
        # cast a ray into the scene
        hit, loc, normal, index, ob, mat = scene.ray_cast(origin, dir)
        
        # the default background is black for now
        color = np.zeros(3)
        if hit:
            color = np.zeros(3)
            light = np.ones(3) * intensity  # light color is white
            for lamp in lamps:
                # for every lamp determine the direction and distance
                light_vec = lamp.location - loc
                light_dist = light_vec.length_squared
                light_dir = light_vec.normalized()
                
                # cast a ray in the direction of the light starting
                # at the original hit location
                lhit, lloc, lnormal, lindex, lob, lmat = scene.ray_cast(loc+light_dir*eps, light_dir)
                
                # if we hit something we are in the shadow of the light
                if not lhit:
                    # otherwise we add the distance attenuated intensity
                    # we calculate diffuse reflectance with a pure 
                    # lambertian model
                    # https://en.wikipedia.org/wiki/Lambertian_reflectance
                    color += intensity * normal.dot(light_dir)/light_dist
        buf[y,x,0:3] = color

# pixels is a flat array RGBARGGBRGBA.... 
# assign to a single item inside pixels is prohibitively slow but
# assigning something that implements Python's buffer protocol is
# fast. So assiging a (flattened) 1024x1024x4 numpy array is fast
output.pixels = buf.flatten()

I have added quite some comment in the code itself and will elaborate on it some more in future articles. For now the code is given as is. You can experiment with it if you like but you do not have to type it in nor create a Scene that meets all the assumptions in the code, you can download a .blend file that contains the code if you like.

Code availability

The files are available from my GitHub repository:

The code itself

A .blend file with a full scene and the code embedded as a text file (click Run Script inside the text editor to run it)