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Important NotesWebsite for Assignment #2
https://course.cse.ust.hk/comp341/S10/Password_Only/projects/project2/index.html
You should use C++ and not use OpenGL
Due: Monday 12 April, 12 pm (noon)Demo: 12 and 13 April in 4221
Grouping: You can change your group if you wish
Grading Scheme (Total: 100%)Loading scene file (10%)Ray tracing (45%)
Scene preparing (5%)Ray-intersection (20%)Shadow casting (5%)
Saving output image (10%)Bells and whistles (35%)
Posted on the web, please check the details
OutlineOverview of Ray TracingMain AlgorithmLoading Scene FileHow to Define Eye RayRay-intersectionLighting ModelSaving Output ImageBells and Whistles
Overview of Ray TracingLoad a scene fileRay traceSave output image
Input: Scene FileOutput: Image File
Overview of Ray TracingBackward ray tracing
EfficientShoot rays from eye to the image plane
Capture the scene
Overview of Ray TracingOne level ray tracing
Ambient light sourceDirectional light sourceShadow casting
Main Algorithmfor each pixel in the image
create a ray from eye_position to the center of the pixelset nearest_t = infinityset nearest_object = NULLset surface_point = NULLfor every objects in the scene
if ray intersects this_object and t < nearest_tset nearest_t = tset nearest_object = this_object
end ifset pixel_color = background colorif nearest_object != NULL
set surface_point = eye_poistion + t * ray_directionfor each light source
if this surface_point is not in shadow pixel_color += compute_shading()
end ifend ifdone
done
Loading Scene FileC++ I/O Stream4 types of data section
ViewerLightSphereTriangle
The first line is comment started with #Between each section in the file, there are exactly one
blank line as a separator
Loading Scene File# comment line
<id #>) <id> <number>
<Property id> <Property values>
Loading Scene File – Viewer 1) VIEWER
EYE_POS 0.0 0.0 3.0 eye position in 3D
VIEW_AT_POS 0.0 0.0 0.0 position in 3D viewed by the eye
VIEW_UP_VEC 0.0 1.0 0.0 view up vector
FOVX 1.5707963 field of view along x radian)
FOVY 1.5707963 field of view along y (radian)
RESOLUTION 256 256 resolution of ray traced image
Loading Scene File – Light 2) LIGHT 2
there are two light sources
TYPE LS_AMBIENT ambient light source
COLOR 0.2 0.2 0.2 RGB value [0,1]
TYPE LS_DIRECTIONAL directional light source
DIR 1.0 1.0 1.0 light going from this direction
COLOR 0.8 0.8 0.8 RGB value [0,1]
Loading Scene File – Sphere 3) SPHERE 3
there are 3 spheres
CENTER 0.0 0.0 0.0
RADIUS 1.0
KD 0.3 0.0 0.0 diffuse component
KS 0.5 0.5 0.5 specular component
N 5.0 shininess
. . .
Loading Scene File – Triangle 4) TRIANGLE 2
there are 2 triangles
VERTEX1 -1.0 -1.0 -1.0 each has three vertices
VERTEX2 1.0 -1.0 -1.0
VERTEX3 -1.0 -1.0 1.0
KD 0.0 0.0 1.0 diffuse component
KS 0.3 0.3 0.3 specular component
N 10.0 shininess
. . .
How to Define Eye Ray
How to Define Eye Ray
How to Define Eye Ray
How to Define Eye Ray
Ray-intersectionParametric ray: r(t) = p + t d
t ≥ 0||d|| = 1, thus t is distance traveled from p in d direction
Implicit object: f(x) =0Intersection occurs when f(r(t)) = 0
Real function of one real variable tSo, intersection ≡ root finding
Intersect with TriangleApproach 1:
Intersect the ray with the plane containing the triangleThen determine whether or not the intersection point is
within the triangleApproach 2:
Consider a ray as an origin and a direction vectorDefine the triangle as a tuple of vertices [v0, v1, v2]
Intersect with Triangle Parametric ray: r(t) = p + t dParametric plane: (x - v0) · (v1 × v2) = 0
Solve (p + t d - v0) · (v1 × v2) = 0
Verify x0 is inside the triangle
s1 × u1, s2 × u2, s3 × u3 are pointing at the same direction
Hard to implement and inefficient
Intersect with Triangle Barycentric coordinates
Any point in a triangle can be defined as P(a, b, c) = c v0 + a v1 + b v2
where, a + b + c = 1 and a, b, c ≥ 0
So,p + t d = (1-a-b) v0 + a v1 + b v2
Solve t, a, bCheck 0 ≤ a ≤ 1, 0 ≤ b ≤ 1 and a + b ≤ 1
Easy to implement and efficient
Intersect with SphereParametric ray: r(t) = p + t dParametric sphere: ||x – c||2 = r2
Solve ||p + t d – c||2 = r2
(t d + p – c) · (t d + p – c) – r2 = 0Test discriminant Δ to find the number of roots
Test for intersection!
Δ = (2 d · (p – c))2 – 4 ((d · d)(p – c) · (p – c) – r2)
dd
cpd
2
))(2(t
Blinn-Phong Lighting Model
Directional Light Source
Directional Light SourceLa = intensity of ambient light source
Simulate indirect global illuminationDoes not varies with lighting or viewing direction
Li = intensity of the i-th directional light source
kd = diffuse material property
ks = specular material property
Directional Light Source
Diffuse termSimulate reflection occurring on dull surfacesVaries only with lighting direction
Specular term:Simulate reflection occurring on smooth surfacesVaries with both lighting and viewing direction
Directional Light Source
Directional Light Source
Saving Output ImageSave output as PPM imageView the output using IrfanView Use C++ I/O Stream with binary flag on
#include <iostream>
std::ofstream fout;
fout.open(“my_image.ppm”,ios::binary);• Write binary number to the file stream
PPM File FormatP6
Magic number for identification
256 256Width, Height
256Maximum value of a unit
<R><G><B><R><G><B>... Image as a sequence of R, G, B tuple
