Demystifying the 3D Rendering Pipeline — Part 1: Modeling & Transformation

Published in

XRPractices

5 min readMar 16, 2024

In 3D computer graphics and 3D game development, the rendering pipeline is the backbone for generating visually immersive experiences. It comprises a series of intricate steps and algorithms, and understanding the rendering pipeline is crucial for xr/game developers and graphics programmers.

In this series I will delve into each stage of the 3D rendering pipeline, exploring the underlying concepts, workflows, and algorithms at a high level starting with modeling and transformation.

1. Modeling

Modeling is the process of creating virtual objects and scenes within a 3D environment. This step involves defining geometric shapes, vertices, edges and faces that compose the objects. Techniques such as polygonal modeling, spline modeling, and procedural modeling are employed to sculpt intricate designs. For instance, consider a simple cube represented by its vertices and faces

Primitive Modeling

This approach utilizes basic geometric shapes like spheres, cubes, cones, and cylinders. These primitives are then combined and modified to form more complex objects. This method is often used for creating the base structure of objects or for simple-level design elements.

Tools: Almost all 3D modeling software offers primitive modeling functionalities. Some popular examples include:

Blender https://www.blender.org/download/
Autodesk Maya https://www.autodesk.com/products/maya/overview
SketchUp https://www.sketchup.com/

Polygonal Modeling

This technique builds complex shapes by manipulating individual polygons (faces formed by vertices and edges). Adjusting the vertex positions and the number of polygons allows for detailed sculpting and creation of organic shapes.

Tools: This method is widely used in professional game development and animation. Popular choices include:

Autodesk 3ds Max https://www.autodesk.com/products/3ds-max/overview
ZBrush https://www.maxon.net/en/zbrushcore
Modo https://www.foundry.com/products/modo/new-releases

Sculpting

Sculpting software allows you to manipulate digital clay, pushing, pulling, smoothing, and pinching your way to intricate forms. It offers a more artistic and intuitive approach compared to the precise control of polygonal modeling.

Tools: This method is widely used in creating organic shapes, concept art rapid prototyping, and high-detail models. Popular choices include

ZBrush https://www.maxon.net/en/zbrushcore

NURBS Modeling

NURBS (Non-uniform rational B-splines) represent smooth curves and surfaces using mathematical formulas. This approach offers precise control over the shape and allows for the easy creation of complex, organic forms.

Tools: NURBS modeling is prevalent in industrial design and engineering applications. Some notable software options include:

Rhinoceros 3D https://www.rhino3d.com/
Autodesk Alias https://www.autodesk.com/products/alias-products/overview
CATIA https://www.3ds.com/3dexperience

Choosing the Right Tool

The selection of a modeling tool depends on the specific needs of the project. Here’s a general guideline:

For beginners: Starting with software that offers a good balance of primitive and polygonal modeling capabilities like Blender or SketchUp is recommended.
For organic shapes and detailed sculpting: ZBrush excels in this domain.
For precise control and engineering applications: NURBS-based software like Rhinoceros 3D is preferred.

These are just a few examples, and numerous other specialized modeling tools cater to specific workflows and industries.

By understanding the different modeling techniques and the tools associated with them, you gain a broader perspective on the initial stage of the 3D rendering pipeline.

2. Transformation

Transformations are a fundamental concept in the 3D rendering pipeline. They allow you to position, rotate, and scale 3D models within the virtual world, creating the illusion of movement and depth.

There are three main types of transformations in 3D graphics:

1. Translation

This involves moving a model along the X, Y, and Z axes in the 3D space. This transformation is represented by a 4x4 matrix known as the translation matrix.

Where (Tx, Ty, Tz) are the translation components representing the amount of displacement along the x, y, and z axes respectively.

To apply translation to a point represented by a vector [x, y, z, 1], we multiply it by the translation matrix

2. Rotation

Rotation involves rotating an object around a specified axis. Rotations can be performed around the x, y, or z axis (or a combination thereof). Each rotation is represented by a rotation matrix.

For example, a rotation around the z-axis by an angle θ is represented by the following rotation matrix.

To apply rotation to a point represented by a vector [x, y, z, 1], we multiply it by the rotation matrix.

3. Scaling

Scaling involves resizing an object along the x, y, and z axes. Similar to translation and rotation, scaling is represented by a scaling matrix.

Where Sx, Sy, and Sz are scaling factors along the x, y, and z axes respectively.

To apply scaling to a point represented by a vector [x, y, z, 1], we multiply it by the scaling matrix.

Here I have touched upon only the first two-phase or steps in the rendering pipeline. There are other steps as well: clipping, projection, rasterization, visibility determination, shading, texturing and finally rendering which I will cover very soon.