Procedural Surface: Exploring Texture Generation and Analysis in Computer Vision

By Fouad Sabry

What is Procedural Surface

In computer graphics, a procedural surface is a representation of a surface as a mathematical implicit equation, rather than an explicit representation.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Procedural surface

Chapter 2: Ray casting

Chapter 3: Solid modeling

Chapter 4: Polygon mesh

Chapter 5: Freeform surface modeling

Chapter 6: Triangulated irregular network

Chapter 7: Surface (mathematics)

Chapter 8: Computer representation of surfaces

Chapter 9: 3D modeling

Chapter 10: Vanishing point

(II) Answering the public top questions about procedural surface.

(III) Real world examples for the usage of procedural surface in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Procedural Surface.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 13, 2024

Book preview

Chapter 1: Procedural surface

A procedural surface is a representation of a surface in computer graphics that is a mathematical implicit equation rather than an explicit depiction of the surface.

An explicit representation, for instance, defines a line as the segment that is straight and passes through two locations that have been previously specified. A surface that is specified as a procedure is referred to as a procedural surface.

An offset surface, for instance, might be considered a procedural representation in computer-aided design (CAD) and computer-aided manufacturing (CAM) milling applications. This is due to the fact that it is defined as the surface that is a fixed distance from another surface. With a 3D body, the silhouette edge is yet another well-known procedural edge that can be found. An edge is defined as the collection of points on a surface whose outwards surface normal is perpendicular to the view vector. This edge is characteristic of a surface.

An additional illustration of a procedural surface is a blob, which may be seen in films such as The Abyss in the scene where the creature that is composed of water reaches out and touches the character. The surface is defined as a surface that exists when two or more control points are orientated in such a way as to make the contribution potential exceed a specific threshold. This is the definition of the surface. Due to the fact that the calculation of such procedural surfaces requires a significantly greater amount of computing power, they are typically utilized in pre-rendered applications rather than real-time ones.

This method is frequently utilized by structural chemists, and it was initially described by van der Waals when he was attempting to identify a region of space in which the electric charge equipotential surface had a fixed value.

{End Chapter 1}

Chapter 2: Ray casting

The theoretical foundation for 3D CAD/CAM solid modeling and image rendering is ray casting. It works similarly to ray tracing in computer graphics, where virtual light rays are cast or traced from a camera's focal point via each pixel in the camera sensor to identify what is visible along the ray in the 3D scene. Scott Roth coined the phrase Ray Casting while working at the General Motors Research Labs from 1978 to 1980. For a thorough discussion of solid modeling techniques, refer to his paper, Ray Casting for Modeling Solids. Roth's ray casting approach was used to construct a U-Joint using cylinders and blocks in a binary tree in 1979.

Prior to the development of ray casting (and ray tracing), computer graphics techniques projected surfaces or edges (such as lines) from the 3D environment onto the image plane, where visibility reasoning had to be used. The world-to-image plane projection, also known as a 3D projection, affine transformation, or projective transform (Homography), is a 3D homogeneous coordinate system transformation. With concealed surface/edge removal, it is difficult to render an image in such manner. Additionally, because ray casting automatically creates silhouettes of curved surfaces, there is no need to manually solve for them everytime the view changes.

Because a line changes to a line, ray casting substantially simplified the picture rendering of 3D objects and scenes.

So, instead of rendering the 3D scene's curving edges and surfaces to the 2D picture plane, The items in the scene are crossed by modified lines (rays).

A 4x4 matrix is used to depict a homogeneous coordinate transformation.

The mathematical method is used in geometric modeling and computer graphics.

Three axes are rotated as part of a transform, independent axes-wide scaling, 3D translations, as well as skewing.

Matrix arithmetic makes concatenating transforms simple.

to be utilized with a 4x4 matrix, [X] represents a point, Y, Z, 1] and a direction vector is represented by [Dx, Dy, Dz, 0].

(Translation is the fourth term, which does not apply to direction vectors.)

The most fundamental ray casting rendering approach makes use of the ray tracing geometric algorithm. Ray tracing-based rendering methods convert three-dimensional situations into two-dimensional graphics by working in image order. To sample the light (radiance) moving in the ray direction toward the observer, geometric rays are traced from the observer's eye. Ray casting is quick and easy since it calculates the color of the light without recursively tracing more rays to sample the incidence radiance on the location the ray touched. This makes it impossible to display reflections, refractions, or the natural falloff of shadows precisely; nevertheless, all of these features can be somewhat simulated with the help of inventive texture map utilization or other techniques. Early real-time 3D video games used ray casting as a convenient rendering technique due to its quick calculation speed.

Consider an image as a screen door, with each square in the screen being a pixel. The principle behind ray casting is to trace rays from the eye, one per pixel, and discover the closest object blocking the passage of that ray. The item that the eye sees as a result of that pixel is this. This algorithm can determine the shade of this object using the material qualities and the impact of the scene's lights. In order to make things simpler, it is assumed that if a surface confronts a light, the light will pass through it without being blocked or casting a shadow on it. Traditional shading models for 3D computer graphics are used to calculate the surface's shading. Ray casting had the advantage of dealing with non-planar surfaces and solids, like cones and spheres, much more easily than prior scanline methods. Ray casting can be used to render any mathematical surface that a ray can intersect. Utilizing solid modeling techniques, complex objects can be simply displayed.

According to the paper's abstract, Ray Casting for Modeling Solids, Virtual light beams are cast as probes to visualize and examine the composite solids that were modeled. Because it is so straightforward, ray casting is dependable and expandable. Finding the points at which a line and a surface connect is the most challenging mathematical task. Therefore, the primitive solids may be constrained by surfaces such as planes, quadrics, tori, and possibly even parametric surface patches. Here, questions related to ray casting's effectiveness and sufficiency are discussed. The major obstacle is a quick picture production capacity