raytracer_cpp

By: Oscar Sharaz Spencer

ray tracer written in pure c++, which generates and renders simple three-dimensional objects. as this project is pretty hefty, myself and Darius Desta have created thorough documentation for you to read. enjoy some renders!

Table of Contents

• 1.0 must know 3D vector math operations
  • 1.1 nature of 3d vectors
  • 1.2 3d vector dot products (scalar output)
  • 1.3 3d vector cross products (vector output)
  • 1.4 normalized vector reflection equation
• 3.0 setup and usage
  • 3.1 cloning
  • 3.2 g++ compiling
• 4.0 contributions and suggestions

Must Know Operations

in this section, I'll be going over the must know mathematical concepts that one must grasp to understand the functionality of this ray tracer.

The Nature of Vectors

Three-dimensional (3D) vectors are mathematical entities used to represent quantities that have both magnitude and direction in three-dimensional space. They are fundamental in ray tracing, in a 3D space, objects, positions, directions, and movements are defined using coordinates and vectors. Three-dimensional vectors are used to represent points in space, directions of rays, positions of lights, positions of objects, and more.

Vector Dot Products

The dot product, also known as the scalar product, is an operation that takes two 3D vectors and produces a scalar (single numerical value) as its result. The dot product is used to determine the similarity or alignment of two vectors and provides information about the angle between them. Here's how to calculate the dot product of two 3D vectors, typically denoted as A and B:

Given two 3D vectors:

$A = (Ax, Ay, Az)$
$B = (Bx, By, Bz)$

The dot product $A · B$ is computed as: $A · B = (AxBx) + (AyBy) + (AzBz)$

Vector Cross Products

The cross product, also known as the vector product, is an operation that takes two 3D vectors and produces a third vector as its result. This new vector is orthogonal (perpendicular) to both of the original vectors and provides valuable geometric information about their relationship. Here's how to calculate the cross product of two 3D vectors, typically denoted as A and B:

Given two 3D vectors:

$A = (Ax, Ay, Az)$
$B = (Bx, By, Bz)$

Calculate the x-component of the resulting vector: $AyBz - AzBy$

Calculate the y-component of the resulting vector: $AzBx - AxBz$

Calculate the z-component of the resulting vector: $AxBy - AyBx$

Vector Reflection Equation

The normalized vector reflection equation is used to calculate the direction of a vector after it reflects off a surface. This is a common concept in physics, computer graphics, and geometry, especially when dealing with light or objects bouncing off surfaces. The equation involves three main components: an incident vector, a surface normal vector, and the reflected vector.

Incident Vector $(I)$: The incident vector represents the initial direction of a vector, such as a ray of light or an object's velocity, before it interacts with a surface. The incident vector is typically denoted as I.

Surface Normal Vector $(N)$: The surface normal vector represents the direction perpendicular to the surface at the point of reflection. It is often denoted as N. A surface normal vector is always a unit vector, meaning it has a magnitude of 1, to ensure it represents only the direction.

Reflected Vector $(R)$: The reflected vector represents the direction of the vector after it reflects off the surface. It is often denoted as $R$.

The normalized vector reflection equation is typically expressed as follows: R = $(I - 2)(I · N)N$

Setup and Usage

in this section, I'll be going over how to get, compile, and run this ray tracer, as well as other information.

Cloning

to download the project locally, copy/paste and run the following in cmd:

git clone https://github.com/oskccy/raytracer_cpp.git
ls

GPP Compiling and Executing

to view the code's render (default or your own designs), install the g++ compiler then run:

cd raytracer_cpp
ls
g++ main.cpp

depending on your designs, this command could result in a 1 - 10 minute hang. (room for contributions here lmao)

macOS/Linux:

ls
open render.ppm

Windows:

ls
start render.ppm

Contributions and Suggestions

contributing to this project would mean the world to me. make this better, sumbit pull requests, because im not a genius. thank you so much!