How to Work With Twisted Quads and Avoid Self-intersections

In 3D modeling, a quad refers to a polygon with four vertices and four edges. It is a fundamental geometric shape used to create surfaces and define the structure of 3D models. Quads are essentially foundational elements in 3D modeling, offering predictability and control over geometry, shading, and deformation.

Twisted Quads

Twisted quads are a specific type of polygon commonly encountered in 3D modeling and computer graphics. Unlike regular quads, which have planar faces formed by four vertices, twisted quads exhibit non-planar faces due to the misalignment of their vertices. This misalignment causes the quad to twist in space, leading to various challenges in rendering, animation, and other aspects of 3D modeling.

Causes of Twisting

Improper Vertex Arrangement: Unequal edge lengths or vertex misalignment can cause twisting.
Non-Planar Faces: Changes in vertex normals or unbalanced edge angles result in non-planar quads.
Articulation and Deformation: Complex joint movements or deformation in animations can lead to twisting.

Effects and Consequences

Rendering Artifacts: Twisted quads can cause shading inconsistencies, unintended highlights, and shadows in rendered images.

Texture Distortion: Applying textures becomes challenging, often resulting in stretching or warping.

Animation and Rigging Issues: Twisting can lead to unnatural deformations during animations or difficulties in weight painting.

Physical Production Challenges: In 3D printing or manufacturing, twisted quads can lead to unexpected outcomes.

Importance of Addressing Twisted Quads

Realism and Aesthetics: Properly aligned quads contribute to realistic and visually pleasing models.

Deformation and Animation: Avoiding twisting enhances natural deformations and animation behavior.

Texture Mapping: Twisted quads complicate accurate texture application, affecting the final look of a model.

Production Efficiency: Working with non-twisted quads streamlines various processes, from rendering to manufacturing.

Self-Intersection

Self-intersections occur when a model's geometry intersects or overlaps with itself. This phenomenon can lead to various issues in rendering, animation, and manufacturing, as it creates unrealistic and unintended visual artifacts. Self-intersections can happen with any type of 3D object, from simple shapes to complex characters and environments.

Causes of Self-Intersection in 3D Modeling

Self-intersections in 3D modeling can occur due to various reasons, often stemming from the complexity of the model, improper techniques, or unintended consequences of transformations. Here are some common causes of self-intersections in 3D modeling:

Complex Geometry: Complex models with intricate details and overlapping parts are more prone to self-intersections. Excessive use of small polygons or fine details can create overlapping areas when surfaces are deformed or manipulated.
Inadequate Topology: Poorly planned topology, such as irregular edge loops or uneven spacing, can lead to parts of the model intersecting during deformations or animations. Sudden changes in edge density can result in overlaps.
Extreme Transformations: Applying extreme scaling, rotation, or translation to a model can cause parts of the geometry to intersect. This is particularly evident when objects are scaled negatively or rotated in ways that cause overlapping.
Animation and Deformation: During animations, limbs or body parts might intersect due to improper rigging, skinning, or weight painting. Complex deformations, especially those involving joints and bones, can lead to unintended self-intersections.
Boolean Operations: Boolean operations used to merge or subtract shapes can result in overlapping geometry if not executed correctly. Failing to clean up or optimize geometry after boolean operations can contribute to self-intersections.
Non-Manifold Geometry: Non-manifold geometry, where edges or vertices don't adhere to standard geometry rules, can result in unexpected intersections. Edges shared by more or fewer than two faces can cause self-intersections.

How to Work With Twisted Quads and Avoid Self-intersections

Create or Import an Object

Launch SelfCAD

In this case, we are using a cube by selecting a cube from the "3D Shapes" tool from the toolbar.

Customize the cube to have details as follows:

Edit Details

To create quads, Add Vertices on the corner faces of the cube.

Click on the Modify Tool, select Edit Details > Add Vertex, and click the middle of the faces where to add vertices as shown below:

Next, add vertices on both the top and side faces of one side,

and only the top faces on the other side

The two different sides will give us a contrast of the operation of each quad.

Next step, activate the Edge Selection tool on the right panel (as shown by the blue arrow) and select the center edges of the cube (shown by the blue ovals below).

Then Scale it by changing our Z from 200 to 10 in the Size parameters, and Move it down by changing the Y from 84 to 80 in the Position parameters, displayed at the left down corner of the workspace:

Change the parameters to:

After applying the above parameters, this is how the cube will look like:

At the top vertices, everything is fixed, and the cuts are regular and easy to modify.

On one side where we inserted vertices on both top and side faces, you can easily Scale and Move them together without any deformation by activating the Vertex selection on your right-hand side, select the vertices you want to operate on by dragging from right to left:

You can change the parameters to either Move and Scale them as you wish or basically use the Scale Tool and Move Tool.

Moving and scaling the selected vertices still forms an intact model of your choice with no complications arising.

The process of Moving and Scaling is smooth because there are cuts already made. As you can see the top faces are nicely fixed also, and no challenge of folding, flipping, or even self-intersection.

On the other side where we only made the vertices at the top faces of the cube, the faces appear as follows, and appear a bit twisted:

Two operations can be done:

First, you can add the cut as follows.

In the Modify Tool, select the Edit Tool > Add Edge and use the cursor to add the edge to make the cut:

Secondly, you can add the vertices and then use the vertices to modify the face.

To do this, in the Modify Tool, select Edit Details > Add vertex and this action will deform the quad depending on where you make the cut because it is as shown.

This is how you may use SelfCAD software to work on the quads in 3D modeling to prevent folding, self-intersection, and flipping out of your design.

Emphasis on the Significance of Proper Quad Topology and Self-intersection Avoidance

The significance of proper quad topology and self-intersection avoidance cannot be overstated in the realm of 3D modeling.

Proper Quad Topology

A well-structured quad topology forms the backbone of any successful 3D model. It underpins the geometry's behavior during deformations, animations, and rendering. When quads are thoughtfully arranged with even edge lengths and aligned vertices, they ensure predictable and smooth transformations. This translates to models that not only look convincing but also respond naturally to changes, enhancing the overall level of immersion. Proper quad topology is not just a technical concern; it's an artistic choice that empowers 3D artists to sculpt and craft their visions with precision and control.

Self-Intersection Avoidance

Avoiding self-intersections is the guardian of realism in 3D modeling. By preventing parts of a model from intersecting or overlapping with each other, we maintain the integrity of the virtual world we're creating. Self-intersections not only disrupt the visual fidelity of models but can also introduce unexpected artifacts and errors in rendering, animation, and physical production. A commitment to self-intersection avoidance demonstrates a dedication to crafting models that are not just superficially impressive but also structurally sound. It ensures that the virtual world adheres to the laws of physics and logical continuity, elevating the quality of the final output.

By establishing proper quad topology, ensuring even vertex distribution, and leveraging subdivision techniques, we empower ourselves to counter the influence of twisted quads, producing models that behave predictably and pleasingly across various applications.