Tag Archives: lambertian

COMP 770 Program 2: Ray Tracing Part 1

Download Project Source/Scenes/Mac-Binaries: Program2.tar.gz


I’ve read about ray tracing a few times in the past, but this assignment gave me a dramatically new perspective on the topic. Two things really struck me about ray tracing. First, what I understood to be ray tracing was actually just ray casting. I didn’t know this while I was implementing the diffuse shaders (pure Lambertian, Blinn-Phong, and Blinn-Phong with Ambience), and so I was rather impressed with the results. However, as soon as I implemented specular reflection via recursion, I started to realize that ray tracing is indeed a much more significant step over ray casting in terms of realism.

My second dramatic realization was just how expensive ray tracing is. Every feature that I added would drive my render times up. And this was compounded by framebuffer resolution, sampling grid size, number of lights, and number of scene primitives. I found myself switching between implementing new features and then going back and implementing various optimizations just to make the render times tolerable.


For part one of this ray tracer program, I used the COMP 575 assignment as a guideline on features to add beyond the minimum in the COMP 770 assignment. I kept going, adding feature after feature, unaware of whether or not these “extra features” would actually be required for the second part of the assignment or not.


  • Resizable View Rect Dimensions
  • Fully Configurable Camera (position, rotate, FOV)
  • Multiple, Colored Light Support
  • Configurable Background Color
  • Output to PNG
  • Supports both Ray Casting and Ray Tracing
  • Specular Reflection
  • Dielectric Reflection and Transmission w/ Refraction


  • Lambertian
  • Blinn-Phong
  • Blinn-Phong with Ambient

Super Sampling

  • Configurable Sample Count for Regular, Jittered, and Adaptive
  • Basic
  • Regular
  • Jittered


  • Multi-Processing Support with OpenMP
  • Simplified Scene Intersection Calculations with Normalized Direction Vectors
  • Tracks recursive contribution of color calculations for early recursion termination
  • Adaptive [Jittered] Sampling


  • Timing Instrumentation
  • Can build without OpenGL, OpenMP, and libpng for benchmarking on embedded systems

Building and Usage

I’ve provided a Makefile with the following targets. It has been tested on Mac OSX, Linux (Ubuntu) and Android for ARM.

NOTICE: By default, I build on a system with OpenGL, OpenMP (libgomp), and libpng. If you don’t have those on your system, then use the NO_GL=1, NO_OMP=1, and NO_PNG=1 settings when running make.

Build Targets/Options

  • make – Builds release.
  • make debug – Builds debug.
  • make clean – Cleans src directory and removes objdir directories.
  • make NO_OMP=1 – Won’t attempt to compile using OpenMP. Handy if the system doesn’t have support. Can be used with other NO_*.
  • make NO_PNG=1 – Won’t attempt to compile using libpng. Handy if the system doesn’t have support. Can be used with other NO_*.
  • make NO_GL=1 – Won’t attempt to compile using OpenGL. Handy if the system doesn’t have support. Can be used with other NO_*.


Usage: raytracer [-shader ] [-sampling ] [-samples ] [-background <0xRRGGBBAA>] [-window  ] [-timing] [-noparallel] [-norecursion] [-nodisplay] [-output ] 

       Sets the shader used. Each one builds upon the previous shader. Default = reflective
       Chooses which sampling method to use. Default = adaptive
       Specifies n x n grid of samples to collect. Ignored for basic sampling. Default = 5
  -background <0xRRGGBBAA>
       Sets the background color. Default = 0x000000ff
       Sets the window size to the specified width and height. Default = 500 x 500
       This switch turns on timing output on the console. Default = off
       This switch turns off multiprocessing. Default = on
       This switch turns off recursive ray tracing resulting in simple ray casting. Default = on
       This switch turns the output to the display. Default = on
       This switch causes the ray tracer to output a png image of the renderer scene.

Image Results


Once I started working on support for dielectrics, I wanted to create a reasonably familiar scene so that I could interpret the results better. I placed a large, mostly transparent, smoke-gray sphere in front of the camera. The ground sphere is still somewhat reflective, but the two colored spheres in the background are non-reflective. When viewing this scene, it’s best to use a white background (-background 0xffffffff) in order to see the distortion at the perimeter of the sphere.

	<!-- camera at (0,2,-12) pointed towards the origin -->
	<camera x="0.0" y="2.0" z="-8.0" fov="90.0"
			lookAtX="0.0" lookAtY="2.0" lookAtZ="0.0"
			upX="0.0" upY="1.0" upZ="0.0"/>
	<!-- smoked sphere -->
	<sphere radius="2.0" x="0.0" y="1.75" z="-3.0">
		<color r="0.3" g="0.3" b="0.3" a="0.3"/>
		<material reflectance="0.0" refraction="1.5" phongExponent="0.0"/>
	<!-- blue sphere -->
	<sphere radius="1.25" x="-4.0" y="2.0" z="2.0">
		<color r="0.0" g="0.0" b="1.0" a="1.0"/>
		<material reflectance="0.0" refraction="1.0" phongExponent="16.0"/>
	<!-- green sphere -->
	<sphere radius="1.25" x="4.0" y="2.0" z="2.0">
		<color r="0.0" g="1.0" b="0.0" a="1.0"/>
		<material reflectance="0.0" refraction="1.0" phongExponent="16.0"/>
	<!-- white overhead light -->
	<light x="0.0" y="5.0" z="0.0" ambient="0.25">
		<color r="1.0" g="1.0" b="1.0" a="1.0"/>
	<!-- "ground" sphere -->
	<sphere radius="50.0" x="0.0" y="-50.0" z="0.0">
		<color r="0.75" g="0.75" b="0.75" a="1.0"/>
		<material reflectance="0.3" refraction="1.5" phongExponent="32.0"/>


Of the various optimizations that I implemented, none provided the immediate results that the parallelism through OpenMP. I was definitely embarrassed that I didn’t think of it before the COMP 575 professor mentioned it. I fully anticipated that I would have to refactor my code to be multi-threaded. I was pleasantly surprised to find OpenMP. I had used a similar compiler extension on some Cell Processor development years ago, but OpenMP is much further along in terms of ease-of-use and compiler support. I was so thrilled when I discovered it, that I blogged about it here. With one line in my Makefile and two lines of code, I gained a nearly 75% increase.

Development Challenges

  • Viewing Rect
  • Floating Point Error When Intersecting Light Ray
  • Transparency + Ray Casting = Does Not Compute
  • Floating Point Error Part Deux

Overall, development went really smooth on this project. I was definitely making a lot of hand-gestures while trying to visualize where my cross products would be aiming as I was trying to generate the viewing rect. I didn’t know how to correlate the up vector of the camera with the vector from the camera position to the lookAt point, especially when they weren’t perpendicular. Finally I decided to use the up vector and assume that the camera was looking straight forward, along it’s z axis. Without this assumption, I felt like I would have to be dealing with an oblique projection, which I wasn’t ready for.

I struggled a little when I was trying to calculate intersections with the scene for the light vector from the visible point back to the light source. Initially I tried to throw out intersections with the primitive that the visible point was on. Of course, that didn’t yield results, so I finally settled on throwing out all intersections that were closer to the visible point than a particular threshold, lambda. The next lecture, the same strategy was mentioned as a solution to that problem.

The next significant problem that I phased was how to deal with transparency. Again, I was unlucky enough to be a little early to implement this feature. Two lectures later, we discussed ray tracing vs. ray casting. Recursive ray tracing, makes reflection and transmission with refraction nearly trivial. For a while, I was a little confused between specular reflection and dielectric reflection, but I finally differentiated the two and accepted the fact that an object can be a dielectric and also have specular reflective material properties. The last part of ray tracing that was really challenging, was the calculation of the “a” constant when determining the filtering of light when it is transmitted through a dielectric. The textbook described how the Beer-Lambert Law determined how much light is transmitted, but they said that a constant for each color channel is chosen and that the natural logs from the formula are rolled into that. Furthermore, they mentioned that developer’s often tune this parameter by eye. I settled on a calculation for “a” that took each color channel of the intersected primitive and multiplied it with (1 – alpha) for that color. Visually, I found the results to be satisfactory.

The last hurdle that I faced was again related to detecting intersections that are too close to the visible point. This time, the rays in question were the transmitted/refracted rays. I was still using the threshold from before to eliminate intersections that were too close to the ray origin. However, the threshold value that I was using was very small. I found that several of the refraction calculations involved a lot of floating point math errors that had built up through the multiple calculations and amplified by the recursion. I just relaxed the threshold and the noise was eliminated.