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In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of any surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space.

What is a 3D model?

Three-dimensional (3D) models represent a physical body using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc.

3D Model creation:

Manually

Algorithmically (procedural modeling)

By scanning

Their surfaces may be further defined with texture mapping.

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The process leading to the description of an object (model) through synthesis or sampling.

The model can be used in the rendering and/or in the simulation phase.

Modeling

Only the object surfaces are modeled, i.e. the boundary of the object, not its volume. Almost all visual models used in games and film are surface models

The object is described as a 3D solid. These models define the volume of the object they represent. Solid models are mostly used for engineering and medical simulations, and are usually built with constructive solid geometry

Surface Modeling

Solid modeling

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Object are described as portion of a volume (Constructive Solid Geometry).

Solid modeling

The object gets described as a simple composition of some 3D elementary primitives (spheres, cubes, etc.)

Primitives can be modified through translations, rotations, deformations etc.

Primitives can be composed with boolear operators (and, or, etc.)

This kind of modeling allows to effectively describe simple objects, but it does not lend itself to the description of complex objects due to the high computational weight of the 3D objects described in this way.

The basic unit of this type of modeling are voxels (volume elements) and objects are described as a composition of these units.

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Surface modeling

Points in 3D space, called vertices, are connected by line segments to form a polygon mesh.

This method is well suited to scanline rendering and is therefore the method of choice for real-time computer graphics.

Polygonal modeling

Surfaces are defined by curves, which are influenced by weighted control points.

Another type of representation widely used is that of Nurbs which arises from a generalization of the Bezier curves; used to create geometric objects, to accurately define their shape.

Is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay.

Material can be added and removed, much like sculpting in clay.

Digital sculpting

Curve modeling

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Surface modeling – Polygonal modeling

Two vertices connected by a straight line become an edge.

Three vertices, connected to each other by three edges, define a triangle, which is the simplest polygon in Euclidean space.

Four sided polygons (generally referred to as quads)and triangles are the most common shapes used in polygonal modeling.

A group of polygons, connected to each other by shared vertices, is generally referred to as an element.

Each of the polygons making up an element is called a face.

A group of polygons which are connected by shared vertices is referred to as a mesh.

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Sampling

Scanning produces a cloud of points, more or less dense depending on the scanner resolution.

Usually, the point cloud is processed to produce a polygonal mesh (the connectivity is computed).

Meshes are usually high-res and need to be simplified in order to be rendered in real-time.

It is possible to directly acquire, through scanning, the shape of an object (and in some cases also colors)