Primitive Curves

Behavior

Creates a straight line segment between two points in 3D space. Default: Start {0,0,0} → End {1,0,0}. Outputs a single Curve. If Start and End are identical, outputs a zero-length curve. Accepts lists - produces one line per point pair using the active list matching mode.

Inputs

Start Point, End Point

Outputs

Curve

Pairs With

Extrude Curve, Offset Curve, Linear Array

Behavior

Creates a line derived from two point pairs - computes the geometric relationship between two line segments defined by (P1,P2) and (P3,P4). Requires all four points. Output depends on the spatial configuration of the two pairs. The resulting line represents the intersection or closest approach between the two implied line segments.

Inputs

Point 1, Point 2, Point 3, Point 4

Outputs

Curve

Pairs With

Construct Point, Intersection 2 Curve

Behavior

Creates a line at the intersection of two planes. The resulting line lies on both planes simultaneously. Requires two non-parallel planes. Parallel planes produce no output. The output line extends infinitely along the intersection direction. If the planes are parallel (no intersection exists), the node returns an empty result.

Inputs

Plane A, Plane B

Outputs

Curve

Pairs With

Construct Plane, Plane XY, Plane XZ

Behavior

Creates a multi-segment line by connecting a sequence of points in order. Optionally closes the shape by connecting the last point back to the first. Close: false. Minimum 2 points required. Points are connected in list order. When Close is true, an additional segment is added from the last point to the first. A single point produces no curve.

Inputs

Points, Close

Outputs

Curve

Pairs With

Construct Point, Curve To Surface, Extrude Curve

Behavior

Creates a smooth curve that passes directly through every given point. The curve is guaranteed to touch each input point. Minimum 2 points. The curve passes through all points in list order. Unlike NURBS Curve, the output always intersects the input points. The degree of smoothness depends on point spacing - closely spaced points produce tighter curvature.

Inputs

Points

Outputs

Curve

Pairs With

Divide By Count, Loft Surface, Pipe

Behavior

Creates a NURBS curve using control points. The curve is attracted to control points but does not necessarily pass through them - producing smoother, more predictable shapes. Minimum 2 control points. Degree is determined automatically from point count. Control points act as weighted attractors. Moving one control point affects the curve locally, not globally. More control points allow finer shape control but increase complexity.

Inputs

Control Points

Outputs

Curve

Pairs With

Control Points, Revolve Surface, Sweep2

Behavior

Creates a NURBS curve with explicit control over points, weights, knots, and degree. Full parametric access to the underlying NURBS representation. Requires matching list lengths for points and weights. Knot vector length must equal points + degree + 1. Weights control how strongly each control point attracts the curve - higher weight pulls the curve closer. Invalid knot/weight combinations produce no output.

Inputs

Points, Weights, Knots, Degree

Outputs

Curve

Pairs With

Control Points, List Sequence

Behavior

Returns a NURBS curve built from control points, degree, and curve type configured directly in the node's input field. Double-click the input field to add a new control point. Click between existing points to insert; toggle between smooth and sharp by clicking the circle/rectangle indicator next to each point. An optional grid with snapping helps align points precisely.

Inputs

Control Points (in-node editor), Degree, Curve Type

Outputs

Curve

Pairs With

Loft Surface, Sweep2, Pipe

Behavior

Generates an intermediate curve between two input curves at a specified parameter (0 to 1). At 0 it matches Curve A, at 1 it matches Curve B, values in between produce a morphed blend. Parameter: 0.5 (midpoint between the two curves). Both input curves should have the same number of control points for predictable morphing. Mismatched curves may produce unexpected intermediate shapes.

Inputs

Curve A, Curve B, Parameter

Outputs

Curve

Pairs With

Range Input, Loft Surface, Linear Array

Behavior

Creates a smooth transition curve that blends between the endpoints of two existing curves with tangent continuity. Connects the end of Curve A to the start of Curve B with G1 tangent continuity. The blend maintains the tangent direction of both input curves at the connection points. If curves are far apart, the blend stretches to bridge the gap.

Inputs

Curve A, Curve B

Outputs

Curve

Pairs With

Join, End Points

Behavior

Creates a circle from a center point and radius on a specified orientation plane. Center: {0,0,0}. Radius: 1. Plane: XY (if not connected). The Plane input controls the circle's orientation in 3D space. Without a plane connection, the circle lies flat on XY. The output is a closed curve.

Inputs

Center, Radius, Plane

Outputs

Curve

Pairs With

Extrude Surface, Pipe, Polar Array

Behavior

Creates a circle that passes through exactly three specified points. Center and radius are computed automatically. Requires 3 non-collinear points. If the three points are collinear, the circle cannot be computed and returns no output. The circle's plane is determined by the three points.

Inputs

Point 1, Point 2, Point 3

Outputs

Curve

Pairs With

Construct Point, Curve To Surface

Behavior

Creates a circle defined by center, a normal vector for orientation, and radius. The normal vector controls which direction the circle faces. Normal: {0,0,1} (facing up). The circle plane is perpendicular to the normal. Unlike Circle which takes a Plane input, this accepts a Vector - easier to orient circles using geometry normals from surfaces or faces.

Inputs

Center, Normal, Radius

Outputs

Curve

Pairs With

Face Normal, Unit Vector

Behavior

Creates the largest circle that fits inside a triangle defined by three points. The incircle is tangent to all three edges. Requires 3 non-collinear points forming a valid triangle. Outputs the circle, its center (incenter), and the computed radius. Degenerate triangles (zero area) produce no output.

Inputs

Point 1, Point 2, Point 3

Outputs

Curve, Center, Radius

Pairs With

Delaunay Mesh, Triangle Panel

Behavior

Creates an ellipse from a center point with independently adjustable major and minor radii. Center: {0,0,0}. Major R and Minor R both default to 1 (producing a circle). When Major R equals Minor R, the output is identical to a Circle. The ellipse lies on the XY plane by default. Output is a closed curve.

Inputs

Center, Major R, Minor R

Outputs

Curve

Pairs With

Loft Surface, Extrude Surface

Behavior

Creates tangent lines from an external point to a circle. Returns the two possible tangent lines touching the circle at one point each. Requires a point outside the circle. A point inside the circle produces no tangent. Always produces exactly two tangent lines for a point outside the circle. If the point is on the circle, produces one tangent line.

Inputs

Point, Circle

Outputs

Tangent Lines

Pairs With

Circle, Join

Behavior

Creates internal tangent lines between two circles - lines that cross between the circles, touching each at one point. Requires two non-overlapping circles. Internal tangents cross the line connecting the two centers. If circles overlap, internal tangents do not exist and the node returns no output.

Inputs

Circle A, Circle B

Outputs

Tangent Lines

Pairs With

Circle, Distance 2 Points

Behavior

Creates external tangent lines between two circles - lines that touch each circle on the outside without crossing between them. Requires two circles that are not concentric (different centers). External tangents exist for any two non-concentric circles, even if they overlap. Concentric circles (same center) have no tangent lines.

Inputs

Circle A, Circle B

Outputs

Tangent Lines

Pairs With

Circle, Join

Behavior

Creates arc segments that are tangent to two existing circles - smooth curved connections with a specified fillet radius. Requires two circles and a fillet radius large enough to bridge both circles. The output arc smoothly connects two circles with tangent continuity at both contact points. If the radius is too small to reach both circles, no arc is produced.

Inputs

Circle A, Circle B, Radius

Outputs

Arc

Pairs With

Circle, Fillet Geometry

Behavior

Creates an arc from a center point, radius, and sweep angle. The arc sweeps counter-clockwise from the starting direction. Center: {0,0,0}. Radius: 1. Angle: in radians (use DegToRad to convert). An angle of 2π (360°) produces a full circle. Negative angles sweep clockwise. The arc lies on the XY plane by default.

Inputs

Center, Radius, Angle

Outputs

Curve

Pairs With

DegToRad, Revolve Surface

Behavior

Creates an arc that passes through three specified points - start, a point on the arc, and end. Requires 3 non-collinear points. The mid point controls the curvature direction - it determines which side of the start-end line the arc bows toward. Collinear points produce a straight line.

Inputs

Start, Mid, End

Outputs

Curve

Pairs With

Point On Curve, End Points

Behavior

Creates an arc defined by start point, end point, and a direction vector at the start. The vector controls the initial tangent. Direction vector determines the arc's departure angle from the start point. The arc leaves the start point in the direction of the vector, then curves to meet the end point. Vector magnitude does not affect curvature - only direction matters.

Inputs

Start, End, Direction

Outputs

Curve

Pairs With

VectorXYZ, Join

Behavior

Creates an arc with additional modification parameters - provides extra control over curvature beyond center/radius/angle. Modifier: 0 (no modification, behaves like standard Arc). The modifier parameter adjusts the arc's shape beyond standard construction. Values away from 0 deform the arc progressively.

Inputs

Center, Radius, Angle, Modifier

Outputs

Curve

Pairs With

Range Input, Loft Surface

Behavior

Creates a rectangle from an origin point (bottom-left corner) with specified width and height. Origin: {0,0,0}. Width: 1. Height: 1. Output is a closed curve. The rectangle extends in the positive X (width) and Y (height) directions from the origin.

Inputs

Origin, Width, Height

Outputs

Curve

Pairs With

Curve To Surface, Extrude Surface, Offset Curve

Behavior

Creates a rectangle defined by two diagonal corner points. Width and height are computed from the point positions. The two points define opposite corners of the rectangle. The rectangle aligns to the XY plane. If both points share the same X or Y coordinate, the rectangle collapses into a line.

Inputs

Point A, Point B

Outputs

Curve

Pairs With

Bounding Box, Extremes

Behavior

Creates a rectangle centered on a given point, expanding equally in all directions by half the width and height. Center: {0,0,0}. Width: 1. Height: 1. The center point is the geometric center of the rectangle, not a corner. The rectangle extends ±width/2 and ±height/2 from center.

Inputs

Center, Width, Height

Outputs

Curve

Pairs With

Centroid, Rectangular Array

Behavior

Creates a rectangle defined by three points - two points define one edge, the third defines the perpendicular extent. Points 1-2 define the base edge. Point 3 sets the height perpendicular to that edge. The rectangle aligns to the direction of the base edge (P1→P2), not to the global axes. This allows creating rectangles at arbitrary angles.

Inputs

Point 1, Point 2, Point 3

Outputs

Curve

Pairs With

Construct Point, Curve To Surface

Behavior

Creates a regular polygon with a specified number of sides inscribed in a circle of the given radius. Center: {0,0,0}. Radius: 1. Sides: 6 (hexagon). All sides are equal length and all angles are equal. Sides = 3 produces a triangle, 4 a square, 6 a hexagon. Output is a closed curve.

Inputs

Center, Radius, Sides

Outputs

Curve

Pairs With

Hexagonal Grid, Polar Array, Extrude Surface

Behavior

Creates a regular polygon defined by one edge (two points) and the number of sides. The polygon is constructed outward from the given edge. The edge length is determined by the distance between Point A and Point B. Unlike Polygon (which uses a radius), this constructs from a known edge length. The polygon builds outward perpendicular to the edge direction.

Inputs

Point A, Point B, Sides

Outputs

Curve

Pairs With

End Points, Explode

Behavior

Creates a star shape with alternating inner and outer radii. The number of points controls how many tips the star has. Center: {0,0,0}. Outer R: 1. Inner R: 0.5. Points: 5. Inner R controls the depth of indentations between tips. When Inner R equals Outer R, the output becomes a regular polygon. Output is a closed curve.

Inputs

Center, Outer R, Inner R, Points

Outputs

Curve

Pairs With

Extrude Surface, Polar Array

Behavior

Creates a 3D helical spiral curve with specified radius, pitch (vertical distance per turn), and number of turns. Radius: 1. Pitch: 1. Turns: 3. The helix spirals along the Z axis. Total height = pitch × turns. Increasing turns at constant pitch makes the helix taller. This is one of the few primitive curves that produces 3D geometry by default.

Inputs

Radius, Pitch, Turns

Outputs

Curve

Pairs With

Pipe, Curve Array, Sweep2