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Assignment #3 Build a simple ray tracer
Computing Science CMPT 361
Assignment #3 (30 marks)
Programming part due: April 6, Wednesday, at 11:59 pm.
Problem 1 (30 marks): Build a simple ray tracer
You will be building a ray tracer. It starts with a simple version that works on scenes consisting
only of spheres, and gets expanded to include shadows, reflection, refaction, texture mapping,
and supersampling. For bonus marks, its features can be expanded to handle arbitrary
polygonal environments in an efficient manner.
In all cases, you may work with just a single light source. You can add any number of additional
light sources if you wish, but it is not required.
You can begin with the skeleton code provided on our website.
Read the code and the comments carefully so that you would know exactly where the changes
are to be made. Use “make raycast” to create an executable called raycast. The program
requires between 2 to 8 command line arguments:
./raycast [–u | –d] step_max <options
The option –u (user) should be used if you want to render a scene you created (to be defined
in the function set_up_user_scene() in scene.cpp). To render the default scene, defined in
the function set_up_default_scene() in scene.cpp, use –d. The next argument is an integer
that specifies the number of recursion levels. For example, when step_max = 0, then no
reflected or refracted rays are to be cast. The remaining arguments can be used to turn on
different features of your raytracer. The default, if no flag is provided, is to turn the feature
off. There are a total of six features:
• +s: inclusion of shadows
• +l: inclusion of reflection
• +r: inclusion of refraction
• +c: inclusion of chess board pattern
• +f: enabling diffuse rendering using stochastic ray generations
• +p: enabling super-sampling
For example, the following command produces a ray-traced image, with 5 levels of recursion,
of the default scene with a chess board and it includes shadows, reflections, and refractions.
No supersampling or stochastic ray generation are provided.
./raycast –d 5 +s +r +l +c +r
Note that the option arguments do not have to be specified in any particular order. Ways to
specify the material properties of the spheres, the light source, and other scene parameters
should be clear from the skeleton code sphere.h, sphere.cpp, raycast.cpp, and scene.cpp.
You should define the sphere geometry. Many global variables are used in the program to
simplify things for teaching purposes, but this is poor programming practice. Also, this is code
from a previous instructor, and there is no guarantee that it will be bug-free. Please report
any problems you experience to me, the TA, or the course mail list.
Your tasks: You should complete the following tasks in order.
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
1. [8 marks] Ray-sphere intersection and local reflectance: Complete functions (defined in
the files sphere.h and sphere.cpp) which determine the first sphere that the ray intersects for
visibility. Also, implement the ray tracer to support visible surface ray tracing using Phong’s
local illumination model, shown below, in trace.cpp. You should use the following model to
color a pixel:
𝐼 = 𝐼𝑎𝑘𝑎 + ∑
𝐼𝑚
𝑎 + 𝑏𝛥 + 𝑐𝛥
2
(𝑘𝑑
(𝑛 ⋅ 𝑙𝑚) + 𝑘𝑠
(𝑟𝑚 ⋅ 𝑣)
𝑁)
𝐿
𝑚=1
This is the simplified Phong model where the light falloff factor is taken into consideration. 𝛥
is the distance between the light source and the point on the object. As stated above, you
may use L=1. Do not change the eye position or the placement of the image plane. The image
size and its resolution can be altered as you wish.
You should complete this part of your program first and test it using:
./raycast [–u | –d] 0
2. [4 marks] Shadows: Next, implement shadows in your ray tracer. Add a shadow multiplier
𝑆𝑚for each light source m you have; let 𝑆𝑚be 0 if the object is in shadow from light m, and 1
if it is not.
𝐼 = 𝐼𝑎𝑘𝑎 + ∑
𝑆𝑚𝐼𝑚
𝑎 + 𝑏𝛥 + 𝑐𝛥
2
(𝑘𝑑
(𝑛 ⋅ 𝑙𝑚) + 𝑘𝑠
(𝑟𝑚 ⋅ 𝑣)
𝑁)
𝐿
𝑚=1
This part can be tested using the command:
./raycast [–u | –d] 0 +s
3. [4 marks] Reflections: Augment your ray tracer to take into consideration of directly
reflected light. The material property “reflectance” of a sphere (see sphere.h) specifies how
much reflected light should contribute to the color of a pixel.
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟
where 𝐼𝑃ℎ𝑜𝑛𝑔 is the pixel color computed using the shadowed Phong model (in part 2 above),
𝑘𝑟
is the object’s reflectance, and 𝐼𝑟
is the reflected light accumulated through recursive ray
tracing. This part of your program can be tested using the command:
./raycast [–u | –d] 5 +s +l
for 5 levels of recursion, for example.
4. [4 marks] Chess board: Think about how to add a shiny planar 8×8 chess board to the
default scene with spheres. (Hint: It is probably not necessary to create 64 polygons for this).
The size of the board should be finite to save computational time. Place the chess board
appropriately with respect to the spheres so that in the ray-traced image, one is able to see
multiple interactions among them, e.g., an image of the chess board in the spheres, shadows
on the board, etc. This part may be tested, e.g., using
./raycast [–u | –d] step_max +s +l +c
5. [4 marks]: Refraction: Make the three spheres in your default scene refractive. To
implement refraction, you will probably need to modify some existing data structures given
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
in the skeleton code. So make sure that you have done the previous parts correctly before
attempting this option. You are free to choose material properties for the transparent spheres.
Here is the lighting model, with 𝐼𝑡 being the light hitting the surface due to refraction, and 𝑘𝑡
being the transmissivity of the surface.
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟 + 𝑘𝑡 ∗ 𝐼𝑡
Place the scene description in the function void set_up_user_scene(). This part may be
tested, e.g., using
./raycast –u step_max +s +l +r +c
6. [4 marks]: Diffuse reflections using stochastic ray generation: Generate better diffuse
effects by tracing a number, say 5, of randomly generated reflected rays to simulate the
diffuse-diffuse inter-reflection. You may declare a constant in global.h for the number of
rays. Here, the average intensity of the diffuse reflected rays (𝐼𝑑) is multiplied by the diffuse
reflection coefficient (𝑘𝑑) for the surface:
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟 + 𝑘𝑡 ∗ 𝐼𝑡 + 𝑘𝑑 ∗ 𝐼𝑑
(This is the same 𝑘𝑑 as in the basic Phong model.) This part can be tested, e.g., using the
following command
./raycast [–u | –d] step_max +s +l +r +c +f
7. [2 marks]: Supersampling to reduce aliasing: Generate 5 rays per square pixel, arranged in
a way as shown in the figure below. Compare the result you can obtain against those from the
previous parts, where a single ray through the pixel center is generated per pixel. This part
can be tested, e.g., using the following command
./raycast –u step_max +s +l +r +f +c +p
What to submit: All required C/C++ and header files, along with the Makefile, a README
file in which you clearly state which features your have implemented, and two images (512 ×
512) in PNG format. One image (default.png) is a screen capture of your rendering of the
default scene, and the other one (mine.png) is for the scene you created (with the checker
board and/or transparent spheres).
Your default.png should resemble the image below (no transparency or chess board):
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
Bonus problem [10 marks]:
(a) [5 marks] You are to ray trace a scene with two glass chess pieces along with a glass chess
board extended to infinity (you can use the way you modeled the chess board from Problem
5). Each chess piece is given by a triangle mesh with 800 faces. Four mesh files are given in the
chess_pieces directory.
The format SMF is used to represent the triangle meshes. In the SMF (Simple Mesh Format)
format, a mesh is given by a vertex list followed by a face list. Each line in the vertex list starts
with the character ‘v’, followed by the x, y, and z vertex coordinates. Each line in the face list
starts with the character ‘f’, and followed by three integers indexing into the vertex list. The
vertex indexes start with 1 and are given in counterclockwise order, viewed from the tip of
the triangle’s outward pointing normal. Any comments start with the character ‘#’. The very
first line of the SMF file is of the form “# n m”, where n is the number of vertices and m the
number of faces in the mesh.
You are free to choose material properties to model your objects. You may even use
appropriate textures that you can find. Note that this would involve a texture mapping process,
which you may not want to delve into. The arrangement of the chess pieces should be
somewhat nontrivial so that inter-surface reflections and refractions can be seen. You are
free to choose specific configurations of your scene.
(b) [5 marks] The next key ingredient of your ray tracer that I am looking for is a way to reduce
unnecessary ray-polygon intersections or to speed up the process via other means. You are
free to choose the technique to implement, e.g., octree or other bounding volume hierarchy.
In order to judge the effectiveness of your technique, your program should be able to report
the total number of ray-polygon intersections performed by your program. You should report
this number for a scene with a single chess piece standing on the chessboard, for both the
naïve ray tracer without speedups and one that uses an octree and/or bounding boxes.
What to submit: All required source files, along with the Makefile, and a README. Place all
the source files required for the bonus problem in their own directory called RayChess. In
your README file, you should explain briefly the speedup technique you employed and
report the improvements it is able to achieve. Submit a final, most impressive image of your
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
ray-traced scene called chess_scene.png. Your Makefile should produce an executable
called raychess, by executing make raychess. Any command line arguments needed should
be explained in the README.
Assignment #3 (30 marks)
Programming part due: April 6, Wednesday, at 11:59 pm.
Problem 1 (30 marks): Build a simple ray tracer
You will be building a ray tracer. It starts with a simple version that works on scenes consisting
only of spheres, and gets expanded to include shadows, reflection, refaction, texture mapping,
and supersampling. For bonus marks, its features can be expanded to handle arbitrary
polygonal environments in an efficient manner.
In all cases, you may work with just a single light source. You can add any number of additional
light sources if you wish, but it is not required.
You can begin with the skeleton code provided on our website.
Read the code and the comments carefully so that you would know exactly where the changes
are to be made. Use “make raycast” to create an executable called raycast. The program
requires between 2 to 8 command line arguments:
./raycast [–u | –d] step_max <options
The option –u (user) should be used if you want to render a scene you created (to be defined
in the function set_up_user_scene() in scene.cpp). To render the default scene, defined in
the function set_up_default_scene() in scene.cpp, use –d. The next argument is an integer
that specifies the number of recursion levels. For example, when step_max = 0, then no
reflected or refracted rays are to be cast. The remaining arguments can be used to turn on
different features of your raytracer. The default, if no flag is provided, is to turn the feature
off. There are a total of six features:
• +s: inclusion of shadows
• +l: inclusion of reflection
• +r: inclusion of refraction
• +c: inclusion of chess board pattern
• +f: enabling diffuse rendering using stochastic ray generations
• +p: enabling super-sampling
For example, the following command produces a ray-traced image, with 5 levels of recursion,
of the default scene with a chess board and it includes shadows, reflections, and refractions.
No supersampling or stochastic ray generation are provided.
./raycast –d 5 +s +r +l +c +r
Note that the option arguments do not have to be specified in any particular order. Ways to
specify the material properties of the spheres, the light source, and other scene parameters
should be clear from the skeleton code sphere.h, sphere.cpp, raycast.cpp, and scene.cpp.
You should define the sphere geometry. Many global variables are used in the program to
simplify things for teaching purposes, but this is poor programming practice. Also, this is code
from a previous instructor, and there is no guarantee that it will be bug-free. Please report
any problems you experience to me, the TA, or the course mail list.
Your tasks: You should complete the following tasks in order.
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
1. [8 marks] Ray-sphere intersection and local reflectance: Complete functions (defined in
the files sphere.h and sphere.cpp) which determine the first sphere that the ray intersects for
visibility. Also, implement the ray tracer to support visible surface ray tracing using Phong’s
local illumination model, shown below, in trace.cpp. You should use the following model to
color a pixel:
𝐼 = 𝐼𝑎𝑘𝑎 + ∑
𝐼𝑚
𝑎 + 𝑏𝛥 + 𝑐𝛥
2
(𝑘𝑑
(𝑛 ⋅ 𝑙𝑚) + 𝑘𝑠
(𝑟𝑚 ⋅ 𝑣)
𝑁)
𝐿
𝑚=1
This is the simplified Phong model where the light falloff factor is taken into consideration. 𝛥
is the distance between the light source and the point on the object. As stated above, you
may use L=1. Do not change the eye position or the placement of the image plane. The image
size and its resolution can be altered as you wish.
You should complete this part of your program first and test it using:
./raycast [–u | –d] 0
2. [4 marks] Shadows: Next, implement shadows in your ray tracer. Add a shadow multiplier
𝑆𝑚for each light source m you have; let 𝑆𝑚be 0 if the object is in shadow from light m, and 1
if it is not.
𝐼 = 𝐼𝑎𝑘𝑎 + ∑
𝑆𝑚𝐼𝑚
𝑎 + 𝑏𝛥 + 𝑐𝛥
2
(𝑘𝑑
(𝑛 ⋅ 𝑙𝑚) + 𝑘𝑠
(𝑟𝑚 ⋅ 𝑣)
𝑁)
𝐿
𝑚=1
This part can be tested using the command:
./raycast [–u | –d] 0 +s
3. [4 marks] Reflections: Augment your ray tracer to take into consideration of directly
reflected light. The material property “reflectance” of a sphere (see sphere.h) specifies how
much reflected light should contribute to the color of a pixel.
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟
where 𝐼𝑃ℎ𝑜𝑛𝑔 is the pixel color computed using the shadowed Phong model (in part 2 above),
𝑘𝑟
is the object’s reflectance, and 𝐼𝑟
is the reflected light accumulated through recursive ray
tracing. This part of your program can be tested using the command:
./raycast [–u | –d] 5 +s +l
for 5 levels of recursion, for example.
4. [4 marks] Chess board: Think about how to add a shiny planar 8×8 chess board to the
default scene with spheres. (Hint: It is probably not necessary to create 64 polygons for this).
The size of the board should be finite to save computational time. Place the chess board
appropriately with respect to the spheres so that in the ray-traced image, one is able to see
multiple interactions among them, e.g., an image of the chess board in the spheres, shadows
on the board, etc. This part may be tested, e.g., using
./raycast [–u | –d] step_max +s +l +c
5. [4 marks]: Refraction: Make the three spheres in your default scene refractive. To
implement refraction, you will probably need to modify some existing data structures given
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
in the skeleton code. So make sure that you have done the previous parts correctly before
attempting this option. You are free to choose material properties for the transparent spheres.
Here is the lighting model, with 𝐼𝑡 being the light hitting the surface due to refraction, and 𝑘𝑡
being the transmissivity of the surface.
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟 + 𝑘𝑡 ∗ 𝐼𝑡
Place the scene description in the function void set_up_user_scene(). This part may be
tested, e.g., using
./raycast –u step_max +s +l +r +c
6. [4 marks]: Diffuse reflections using stochastic ray generation: Generate better diffuse
effects by tracing a number, say 5, of randomly generated reflected rays to simulate the
diffuse-diffuse inter-reflection. You may declare a constant in global.h for the number of
rays. Here, the average intensity of the diffuse reflected rays (𝐼𝑑) is multiplied by the diffuse
reflection coefficient (𝑘𝑑) for the surface:
𝐼 = 𝐼𝑃ℎ𝑜𝑛𝑔 + 𝑘𝑟 ∗ 𝐼𝑟 + 𝑘𝑡 ∗ 𝐼𝑡 + 𝑘𝑑 ∗ 𝐼𝑑
(This is the same 𝑘𝑑 as in the basic Phong model.) This part can be tested, e.g., using the
following command
./raycast [–u | –d] step_max +s +l +r +c +f
7. [2 marks]: Supersampling to reduce aliasing: Generate 5 rays per square pixel, arranged in
a way as shown in the figure below. Compare the result you can obtain against those from the
previous parts, where a single ray through the pixel center is generated per pixel. This part
can be tested, e.g., using the following command
./raycast –u step_max +s +l +r +f +c +p
What to submit: All required C/C++ and header files, along with the Makefile, a README
file in which you clearly state which features your have implemented, and two images (512 ×
512) in PNG format. One image (default.png) is a screen capture of your rendering of the
default scene, and the other one (mine.png) is for the scene you created (with the checker
board and/or transparent spheres).
Your default.png should resemble the image below (no transparency or chess board):
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
Bonus problem [10 marks]:
(a) [5 marks] You are to ray trace a scene with two glass chess pieces along with a glass chess
board extended to infinity (you can use the way you modeled the chess board from Problem
5). Each chess piece is given by a triangle mesh with 800 faces. Four mesh files are given in the
chess_pieces directory.
The format SMF is used to represent the triangle meshes. In the SMF (Simple Mesh Format)
format, a mesh is given by a vertex list followed by a face list. Each line in the vertex list starts
with the character ‘v’, followed by the x, y, and z vertex coordinates. Each line in the face list
starts with the character ‘f’, and followed by three integers indexing into the vertex list. The
vertex indexes start with 1 and are given in counterclockwise order, viewed from the tip of
the triangle’s outward pointing normal. Any comments start with the character ‘#’. The very
first line of the SMF file is of the form “# n m”, where n is the number of vertices and m the
number of faces in the mesh.
You are free to choose material properties to model your objects. You may even use
appropriate textures that you can find. Note that this would involve a texture mapping process,
which you may not want to delve into. The arrangement of the chess pieces should be
somewhat nontrivial so that inter-surface reflections and refractions can be seen. You are
free to choose specific configurations of your scene.
(b) [5 marks] The next key ingredient of your ray tracer that I am looking for is a way to reduce
unnecessary ray-polygon intersections or to speed up the process via other means. You are
free to choose the technique to implement, e.g., octree or other bounding volume hierarchy.
In order to judge the effectiveness of your technique, your program should be able to report
the total number of ray-polygon intersections performed by your program. You should report
this number for a scene with a single chess piece standing on the chessboard, for both the
naïve ray tracer without speedups and one that uses an octree and/or bounding boxes.
What to submit: All required source files, along with the Makefile, and a README. Place all
the source files required for the bonus problem in their own directory called RayChess. In
your README file, you should explain briefly the speedup technique you employed and
report the improvements it is able to achieve. Submit a final, most impressive image of your
Computing Science CMPT 361 Spring 2016
Instructor: Tom Shermer Simon Fraser University
ray-traced scene called chess_scene.png. Your Makefile should produce an executable
called raychess, by executing make raychess. Any command line arguments needed should
be explained in the README.
1 file (1.4MB)
