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Subdivision sketch: minimum viable topology.

This is a brief write-up about subdivision artifacts caused by mesh deformation and how segment matching can create topology that reduces the disruption caused by intersecting shapes.

The accuracy of subdivision modeling is limited because it smooths the mesh by averaging the geometry. Adding, merging or moving geometry disrupts the segment spacing of curved surfaces and can deform the mesh. Subtle deformation may be acceptable but severe deformation will likely cause visible smoothing artifacts.

Below is an example of how mesh deformation affects subdivision smoothing when sliding, moving or adding edge segments on a cylinder.

Mesh deformation, around shape intersections on curved surfaces, is often caused by adding support loops that disrupt the segment spacing or by merging the existing geometry into the intersecting geometry. The examples below show what this can look like when the mesh is subdivided.

From left to right: Adding support loops that disrupt the segment spacing near the base of the intersection tends to deform the curvature outwards. Increasing the number of segments and merging them into the support loop at the base of the intersection tends to deform the curvature inwards.

Using the geometry of the curvature to form part of the support loop around the base of the shape intersection greatly reduces the visibility of the smoothing artifact but doesn't completely resolve the deformation that's caused by the inconsistent segment spacing.

Adjusting the shapes, so the edge segments match, will produce a shape intersection with a relatively even polygon distribution. Since the segments in each curve are roughly the same length, the subdivision smoothing will be relatively consistent across all of the connected shapes. Which helps prevent undesired mesh deformation that could cause smoothing artifacts.

Working through these basic topology flow issues early in the block out will make the modeling process a lot easier but sometimes it's not possible to match the segments of each shape perfectly. In most cases though, close is good enough.

Any minor difference between the shapes can usually be taken up by the faces between the outer support loop and the base of the shape intersection. The support loop on the inside of the shape intersection can also be adjusted to compensate for the width of the support loop on the outside of the shape intersection.

Below is an example of the order of operations that works for segment matching most curved shapes. Start by adjusting the shapes until the segments that make up the curve are aligned then cut in the additional loops along the curve. Remember to include the width of the outer support loop when matching the segments.

Basic cylinder intersection: Line up the segments in both shapes until they're close to where the outer support loop will be. Confine any potential difference in the shapes to the area between the inner and outer support loops

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Tapered cylinder intersection: Same as the basic cylinder intersection but a triangular quad can be used to redirect the loop flow where the three shape profiles meet.

Edge to edge cylinder intersection: Rotating the starting position of the intersecting shape can provide better options for directing the topology flow, without having to arbitrarily increase the amount of geometry required.

[Perpendicular] Overlapping cylinder intersection: Complex shape intersections increase the likelihood that some of the support loops will disrupt the curvature and cause smoothing artifacts. Rotating the intersecting shape can help optimize the use of existing geometry as support for the adjacent topology flow but sometimes it's just necessary to increase the number of segments in the shapes to reach the desired level of surface quality.

[Parallel] Overlapping cylinder intersection: Similar to the shapes in the previous example but could also benefit from moving the smaller shape a bit further into the larger one. Sometimes it's necessary to simplify certain details or compromise slightly on the position of the shapes to achieved the desired results when the intersecting shape is constrained by the number of segments in existing mesh.

Increasing the number of segments in a curve can make it easier to route the topology flow across the shape intersections and can also increase the accuracy of the subdivided curve but there are certain situations where details need to be added to an existing mesh that can't be adjusted easily. The same segment matching strategy can be used to find the minimum amount of geometry required to match the intersecting shape to the existing shape, even if the number of segments isn't evenly divisible or if the intersecting cylinder geometry has to be rotated to line up with the existing geometry.

Recap: Block out complex shape intersections before merging and adding support loops. Match the segments of the intersecting shapes and line up the edges of adjacent shapes as support whenever possible. When merging intersecting shapes, avoid deforming the curved surfaces by constraining any differences in the shapes to the area between the inner and outer support loops that define the shape intersection.