Guide to G0, G1, G2, and G3 CAD Surface Continuity

Surface continuity defines how smoothly two curves or surfaces connect to one another in Computer-Aided Design (CAD). Categorized by levels from G0 to G3, geometric continuity dictates the mathematical alignment of adjacent surfaces, directly affecting light reflections, aerodynamics, and structural integrity. Understanding these levels allows designers and engineers to transition from basic mechanical modeling to high-end Class-A surfacing used in automotive and consumer product design.

What Is Geometric Continuity?

In CAD surfacing, the "G" stands for "Geometric." Geometric continuity measures the visual and physical smoothness across the boundary where two surfaces meet. Each progressive level—from G0 to G3—builds upon the constraints of the previous level, increasing the smoothness of the transition and the quality of surface reflections.

G0 Continuity: Positional (Touch)

G0 continuity, or positional continuity, is the simplest connection between two surfaces. It occurs when two surfaces share a common edge, meaning their boundary coordinates match with no gaps.

  • Characteristics: The surfaces touch, but their angles along the boundary can be completely different.
  • Visual Result: A sharp corner, crease, or seam is visible along the joint.
  • Reflections: Light reflections break abruptly at the boundary line.
  • Common Use: Sharp geometric features, basic mechanical parts, and standard structural components where seamless aesthetic flow is unnecessary.

G1 Continuity: Tangency (Angle Alignment)

G1 continuity, or tangent continuity, occurs when two surfaces share a common boundary (G0) and also share a common tangent vector along that edge. This means the surfaces meet at the exact same angle without an abrupt change in direction.

  • Characteristics: The transition across the boundary shares the same slope, eliminating any sharp crease.
  • Visual Result: The seam appears smooth to the touch and the naked eye.
  • Reflections: While the edge appears smooth, zebra stripe analysis or specular reflections will reveal a distinct bend or "kink" at the transition point.
  • Common Use: Standard fillets, rounds, and general consumer product design where high-end optical perfection is not strictly required.

G2 Continuity: Curvature (Curvature Alignment)

G2 continuity, or curvature continuity, requires surfaces to share the same position (G0), the same tangent angle (G1), and the same radius of curvature at the boundary. The rate at which the surface curves is identical on both sides of the seam.

  • Characteristics: There is no sudden step-change in curvature radius across the boundary.
  • Visual Result: An exceptionally smooth transition that appears organic and unified.
  • Reflections: Light reflections and zebra stripes flow seamlessly across the joint without any visible breaks, kinks, or distortion.
  • Common Use: Automotive body panels, ergonomic handles, and high-end consumer electronics (known as Class-A surfacing) where reflection highlights must look uninterrupted.

G3 Continuity: Curvature Acceleration (Torsion)

G3 continuity takes surface smoothness one step further by matching position (G0), tangency (G1), curvature (G2), and the rate of change of curvature—known as curvature acceleration or torsion.

  • Characteristics: The curvature not only matches at the boundary, but it also changes at the exact same rate on either side as it approaches and leaves the transition point.
  • Visual Result: Completely eliminates the subtle "lead-in" flat spots that can sometimes be detected in G2 transitions under critical lighting conditions.
  • Reflections: Zebra stripes and highlights blend effortlessly with maximum fluidity, producing flawless optical performance.
  • Common Use: Supercar exteriors, luxury product casing, optical lenses, and aerodynamic components where even micro-distortions in airflow or light must be eliminated.

Summary

  • G0: Surfaces touch (creates a sharp crease).
  • G1: Surfaces share an angle (smooth seam, broken reflection).
  • G2: Surfaces share a radius (smooth seam, continuous reflection).
  • G3: Surfaces share a curvature acceleration rate (perfect optical flow, zero reflection distortion).