Continuity G0 to G3

Overview#

Continuity describes how two curves or surfaces behave where they meet. The "G" stands for geometric continuity (shape-based, independent of parameterization), as opposed to "C" continuity, which depends on parameter speed. Industrial designers use G levels because the eye sees shape, not parameters.

Fusion exposes G0, G1 and G2 directly in tools such as Patch, Loft and Fillet. Autodesk's help lists only G0, G1 and G2 options; G3 is not a selectable option, so you achieve it indirectly by design (large smooth surfaces, high-quality fillets) and judge it with analysis.

Where to find it#

• Patch: per-edge Connected, Tangent, Curvature.
• Loft: per-profile Connected/Tangent/Smooth (G2) conditions with weights.
• Fillet: Continuity options (Tangent G1, Curvature G2).
• Sweep/Extrude: indirect, through guide rails and tangency options where offered.
• Analysis: Inspect > Zebra, Curvature Comb, Curvature Map.

How each level looks#

G0: positional#

Two faces share an edge. In a shaded view with edges off you see a crease. Zebra stripes meet at the seam but kink or jump. Fine for engineering corners and mechanical edges.

G1: tangent#

The faces share a tangent plane along the seam. There is no crease, but curvature may jump from flat to curved instantly. Zebra stripes cross the seam without a break, but their bend changes abruptly. A fillet with tangent continuity is G1.

G2: curvature#

Curvature matches along the seam, so stripes flow smoothly. Most consumer products target G2 on visible transitions. In Fusion a curvature-continuous fillet or a Smooth loft/patch condition delivers it.

G3: curvature rate#

The rate of change of curvature also matches. Used in automotive class-A surfaces. Autodesk's help documents no G3 control, so rely on well-formed, low-degree surfaces and verify using curvature combs: the comb envelope should vary without a kink in its slope.

Step by step: achieving G2 between two surfaces#

1. Build the two surfaces with edges that meet. If a gap exists, Extend and Trim first.
2. Build a connecting Patch between the edges, or use Loft between the two edges with the first and last conditions set to Smooth/Curvature.
3. Set the continuity to Curvature on both sides; start with default weights.
4. Run Curvature Comb on the connecting patch edges and the neighbors. The comb teeth lengths should match at each joint.
5. Run Zebra and rotate the model. Stripes should flow evenly across both seams.
6. Adjust weights to fix lumps: increasing a weight pushes the patch farther along the neighbor's direction.
7. Stitch the surfaces into the final body. Stitching does not change continuity; it only joins.

Options reference#

Tips and pitfalls#

Tip: Choose the continuity by what the eye sees. Hidden or mechanical transitions seldom need above G1. Highlight areas on a product (shoulders of a bottle, body lines) justify G2.

Tip: Fewer, larger, simpler surfaces make high continuity easier. Many small patches multiply seams that need matching.

Warning: Asking for G2 on every edge of a small patch overconstrains it and causes bulges. Prefer G1 on minor edges.

Warning: Continuity is a property of the edge. Trimming a surface later, or editing neighbors, can silently break a matched seam. Re-run analysis after edits.

Warning: Stitching does not create smoothness. A quilt can be fully closed with G0 seams only.

Tip: When two surfaces already differ in curvature direction (one convex, one concave), a G2 blend needs an inflection; expect an S-shaped patch and check combs for it.

Worked example: blending a 3 mm fillet versus a patch#

Two surfaces meet at a 90 degree corner and you need a rounded transition with a 10 mm blend. Compare outcomes with a tangent fillet and a curvature (G2) fillet.

• A G1 fillet with a constant radius of 10 mm produces a circular arc. Its curvature jumps from 0 on the flat faces to 1/10 = 0.1 per mm on the arc, and back to 0. Zebra stripes bend smoothly but visibly kink where the arc meets the flat.
• A G2 (curvature continuous) blend starts at curvature 0 and ramps gradually, so the zebra stripes flow without a kink. The price is a slightly wider blend that consumes more of the adjacent surfaces.

For a product part that is injection molded and painted, G1 is usually acceptable. For a glossy visible panel under strong reflection, G2 shows its worth. For an aerodynamic skin or a lens, designers go further (G3) but the documented dialogs give you no G3 control, so you rely on good geometry.

Numbers behind the terms#

The numeric thresholds in the right-hand column are working conventions, not Fusion settings; adopt tolerances that suit your manufacturing process.

A concrete example of curvature matching: a 50 mm radius arc has curvature 1/50 = 0.02 per mm. A G2 joint to a spline requires the spline to start with curvature 0.02 per mm, otherwise the comb shows a jump. A G1 joint only requires the tangent direction to match, so the comb jumps from, say, 0.02 to 0.

Failure modes and fixes#

Choosing the continuity per feature#

1. Decide the class of each surface: structural, visible, or aerodynamic.
2. Use G0 for hidden or internal joints and where a crisp edge is intended.
3. Use G1 for most consumer product blends.
4. Use G2 for large glossy faces and where reflections cross the edge.
5. Verify with Zebra and Curvature Comb before moving on, not at the end.

Workflow advice#

• Fix the poorest quality surface first; blends inherit the problems of their neighbors.
• Keep control point counts low on sketch splines; a spline with eight fit points that wiggle will give wiggly curvature no matter which G level you choose.
• Do not combine G2 requirements on both ends of a short patch; there is not enough surface to satisfy both, and the result bulges.

Choosing tolerances for sign-off#

Agree the acceptance criteria before you model, not after. A workable set for a consumer product is: G0 gap under 0.01 mm on stitched edges, G1 tangent deviation under 0.5 degrees on visible seams, and G2 required only on surfaces that carry strong reflections. Record these in the file or a drawing note so a reviewer knows what "continuous" means for this part. A small tangent break is easy to miss in a casual shaded look but obvious in zebra stripes. When a customer asks for 'class A', ask which edges and what deviation they will accept; the answer changes the effort by an order of magnitude.

Why G2 sometimes cannot be achieved#

Curvature continuity demands that the second derivative at the joint matches, which constrains how far the adjacent surface can wander. If one side of the joint is a sphere of radius 20 mm and the other must be a flat plane within 5 mm, curvature jumps from 0.05 per mm to 0 over a tiny region, which no smooth blend of that size can deliver without bulging. The fix is to enlarge the blend zone, change the radius, or accept G1. Recognizing this early saves hours of fiddling with weights.

Practice exercise#

1. Sketch two arcs of different radius that meet at a point with a shared tangent. Surface-extrude each 40 mm.
2. Observe a G1 joint: zebra crosses cleanly but the comb shows a jump of teeth length at the seam.
3. Delete one extruded surface and replace it by a Patch with Curvature continuity on the shared edge, using a surface with some curvature.
4. Compare the combs: the teeth should now match in length across the seam.

Expected: a clear difference between the G1 and G2 joints in both comb and zebra.

Stretch challenge#

Create two lofted surfaces meeting along a 100 mm edge, once with G0 and once with G2 edge conditions, and compare them with Zebra analysis (vertical and horizontal stripes) and a Curvature Comb on a section across the edge. Expected result: with G0 the stripes snap at the edge and the comb shows a vertical jump; with G2 the stripes pass continuously and the comb teeth match in length at the joint. Record the comb scale and density you used so you can compare fairly.

Related#

• Curvature Analysis
• Patch
• Fillet and Replace Face