This topic includes concepts like vectors, matrices, transformations, and geometric algorithms. It helps in creating and manipulating graphical images.
Coordinate systems: Coordinate systems define the position of objects in a 3D space. Understanding them is crucial for graphics programming.
Linear algebra: Linear algebra is a mathematical approach used to handle a large number of data points. It involves matrix operations, vectors, and linear transformations that can be used to manipulate objects in 3D space.
Trigonometry: Trigonometry is fundamental to computer graphics, as it helps understand spatial geometry and 3D transformations. It deals with the relationships between the sides and angles of triangles.
Calculus: Calculus is essential for creating smooth, continuous animations and curves. It is used to compute derivatives and integrals.
3D geometry: Basics of 3D computer graphics, which includes the geometry of objects in 3D space, and their projection onto a 2D space.
Graphics pipeline: Graphics pipeline refers to the process of rendering objects in a 3D space and projecting them onto a 2D screen. It includes rendering, shading, and clipping.
Rendering: Rendering is the process of generating an image from a 3D scene. It is achieved through techniques like ray tracing, rasterization, and more.
Shading: Shading is the process of applying light and color to objects. It involves the use of algorithms and techniques, including texture mapping, bump mapping, and specular shading.
Animation: Animation involves the creation of motion and change over time. This field includes topics like keyframe animation, interpolation, and motion capture.
Graph theory: Graph theory is a branch of mathematics concerned with the study of graphs and networks. It can be used to model relationships between objects in a scene and create efficient algorithms for rendering and simulation.
Data visualization: Data visualization is the graphical representation of information and data. It involves the use of charts, graphs, and other visual tools to help people understand complex data.
Probability and statistics: Probability and statistics are essential for creating realistic and random simulations. Understanding these fields is essential for modeling complex systems or events in a computer program.
Physics: Physics involves the study of natural phenomena and the laws governing them. Physics models can be used to simulate realistic behavior of physical properties of objects, such as mass and force.
Fourier transforms: Fourier transforms are mathematical tools used for analyzing signals or sound. They can be implemented in image processing or filtering to detect edges or contours.
Optimization: Optimization involves the process of finding the optimal solution of a problem, e.g., the fastest or the most efficient. Optimization techniques can be used in graphics programming to optimize computations and rendering.
Linear Algebra: Linear algebra in computer graphics is used to handle geometric transformations such as rotation, scaling, translation, and projection. It is also used for solving systems of equations in physics simulations.
Calculus: Calculus is used in computer graphics for anti-aliasing and to calculate the precise position of curves and surfaces.
Geometry: Geometry plays a fundamental role in computer graphics as it helps in modeling of 3D objects, computing their relative positions and transformations.
Trigonometry: Trigonometry is used in computer graphics to calculate angles, distances, and positions of objects in 3D environments.
Probability and Statistics: Probability and statistics are used to model and simulate complex systems such as particle systems, fluid dynamics, and light transport.
Differential Equations: Differential equations are used in computer graphics to solve complex problems such as fluid dynamics and physics-based simulations.
Topology: Topology is used in computer graphics to define and manipulate the shapes of objects and meshes, and to create smooth transitions between different shapes.
Numerical Analysis: Numerical analysis is used to solve mathematical problems that arise in the field of computer graphics, such as calculating surface normals, interpolation, and approximation techniques.
Optimization: Optimization is used in computer graphics to solve problems such as finding the optimal camera view or the optimal path for a character to walk or drive along a surface.
Graph Theory: Graph Theory is used in computer graphics to model connectivity between vertices of a mesh, and to solve problems such as shortest path finding, and path optimization in particle simulation.