Cutter Profile Evaluation

This spec defines the selected cutter profile algorithms used by drop-cutter, push-cutter, preview mesh generation, and swept-volume simulation.

Selected Cutter Shapes

• Flat end mill.
• Ball nose end mill.
• Bull nose / corner radius cutter.
• Cone cutter / V-bit.
• Ball-to-conical compound cutter.

Inputs

type CamCutterInput = {
  kind: "flat" | "ball" | "bull" | "cone" | "ball-cone";
  diameter?: number;
  cuttingLength?: number;
  shaftLength?: number;
  cornerRadius?: number;
  includedAngleDeg?: number;
  ballDiameter?: number;
  maximumDiameter?: number;
};

Normalized Cutter

Build a normalized cutter before generation:

type CamCutter = {
  kind: string;
  radius: number;
  diameter: number;
  cuttingLength: number;
  shaftLength: number;
  profileHeight: number;
  heightAtRadius(r: number): number | null;
  radiusAtHeight(h: number): number | null;
  segmentAtRadius?(r: number): CamProfileSegment | null;
  segmentAtHeight?(h: number): CamProfileSegment | null;
};

Validation:

• All selected dimensions must be finite and positive.
• cornerRadius < diameter / 2.
• 0 < includedAngleDeg < 180.
• ballDiameter <= maximumDiameter for ball-cone.
• Invalid input returns a generation-stopping error before mesh processing.

Algorithm: Flat Profile

Inputs:

• diameter, cuttingLength.

Derived:

• R = diameter / 2.
• profileHeight = 0.

Functions:

• heightAtRadius(r) returns 0 for 0 <= r <= R, otherwise null.
• radiusAtHeight(h) returns R for 0 <= h <= cuttingLength, otherwise null.

Contact capability:

• Vertex: valid if XY distance <= R.
• Facet: bottom plane or side/shaft where applicable.
• Edge: tangent to a cylinder around the cutter axis.

Algorithm: Ball Profile

Inputs:

• diameter, cuttingLength.

Derived:

• R = diameter / 2.
• Ball center is local (0, 0, R).
• profileHeight = R.

Functions:

• heightAtRadius(r) = R - sqrt(R * R - r * r) for 0 <= r <= R.
• radiusAtHeight(h) = sqrt(R * R - (R - h) * (R - h)) for 0 <= h < R.
• radiusAtHeight(h) = R for R <= h <= cuttingLength.

Contact capability:

• Vertex/facet/edge contacts must respect the spherical bottom.
• Edge contact can use standard ray/cylinder intersection between the ball center path and the triangle edge swept cylinder.

Algorithm: Bull Profile

Inputs:

• diameter, cornerRadius, cuttingLength.

Derived:

• R = diameter / 2.
• Rc = cornerRadius.
• Rf = R - Rc.
• Toroid center ring radius is Rf, local Z center is Rc.

Functions:

• heightAtRadius(r) = 0 for 0 <= r <= Rf.
• heightAtRadius(r) = Rc - sqrt(Rc * Rc - (r - Rf) * (r - Rf)) for Rf < r <= R.
• radiusAtHeight(h) = Rf + sqrt(Rc * Rc - (Rc - h) * (Rc - h)) for 0 <= h < Rc.
• radiusAtHeight(h) = R for Rc <= h <= cuttingLength.

Contact capability:

• Flat center uses flat cutter contact.
• Corner uses circular/toroidal profile contact.
• Edge contact against sloped edges may require a bounded numeric solve.

Numeric solve requirements:

• Use a local bracketed root finder with max iterations and tolerance.
• If convergence fails, skip that candidate and emit a warning.
• Keep the bull-corner solve bounded, deterministic, and covered by convergence tests.

Algorithm: Cone Profile

Inputs:

• maximumDiameter or diameter.
• includedAngleDeg.
• cuttingLength.

Derived:

• R = maximumDiameter / 2.
• A = includedAngleDeg * PI / 360.
• H = R / tan(A).
• profileHeight = H.

Functions:

• heightAtRadius(r) = r / tan(A) for 0 <= r <= R.
• radiusAtHeight(h) = min(R, h * tan(A)) for 0 <= h <= cuttingLength.

Contact capability:

• Tip contact.
• Conical side contact.
• Circular transition/shaft contact above H.

Algorithm: Ball-Cone Profile

Inputs:

• ballDiameter, maximumDiameter, includedAngleDeg, cuttingLength.

Derived:

• Rb = ballDiameter / 2.
• Rmax = maximumDiameter / 2.
• A = includedAngleDeg * PI / 360.
• Tangency radius Rt = Rb * cos(A).
• Ball height at tangency Ht = Rb - sqrt(Rb * Rb - Rt * Rt).
• Cone local height offset is chosen so cone height at Rt equals Ht.

Segments:

• Ball segment for 0 <= r <= Rt.
• Cone segment for Rt < r <= Rmax.
• Shaft segment for heights above the cone top.

Requirements:

• heightAtRadius must be continuous at Rt.
• radiusAtHeight must select the segment whose height interval contains h.
• If ballDiameter == maximumDiameter, treat as a ball cutter plus shaft.

Preview Mesh

Generate plain triangle meshes:

• Revolve profile polyline around the Z axis.
• Use configurable radial segments, default 32.
• Include cutter body and shaft as separate material groups when possible.
• Mesh generation must run in UI or worker without BREP topology.

Swept Segment Mesh

For preview/simulation:

• Flat cutter: cylinder swept along segment with flat end caps.
• Ball cutter: capsule-like swept lower profile plus shaft.
• Bull/cone/ball-cone: acceptable first pass is a conservative triangle mesh generated by sampling profile cross-sections at segment endpoints and along the segment.
• Swept meshes are visualization/collision approximation; exact material removal must not depend on BREP topology.

Tests

• Validate every selected cutter rejects invalid dimensions.
• Verify heightAtRadius and radiusAtHeight round-trip at representative sample points.
• Verify ball-cone continuity at the tangent radius.
• Verify preview mesh has nonzero vertices and triangles for each shape.
• Verify missing or invalid cutter shape data fails validation or receives the selected schema default before generation.