Module: Geom

Overview

Note:

Lines and Planes are infinite.

The Geom module defines a number of Module methods that let you perform different geometric operations.

The methods in this module take lines and planes as arguments. There is no special class for representing lines or planes. Arrays are used for both.

A line can be represented as either an Array of a point and a vector, or as an Array of two points.

line1 = [Geom::Point3d.new(0, 0, 0), Geom::Vector3d.new(0, 0, 1)]
line2 = [Geom::Point3d.new(0, 0, 0), Geom::Point3d.new(0, 0, 100)]

A plane can be represented as either an Array of a point and a vector, or as an Array of 4 numbers that give the coefficients of a plane equation.

plane1 = [Geom::Point3d.new(0, 0, 0), Geom::Vector3d.new(0, 0, 1)]
plane2 = [0, 0, 1, 0]

There are several good books on 3D math if you are new to the concepts of a line, plane, and vector.

Version:

  • SketchUp 6.0

Defined Under Namespace

Classes: BoundingBox, LatLong, Point3d, PolygonMesh, Transformation, UTM, Vector3d

Class Method Summary # collapse

Class Method Details

.closest_points(line1, line2) ⇒ Array(Geom::Point3d, Geom::Point3d)

The closest_points method is used to compute the closest points on two lines.

Examples:

line1 = [Geom::Point3d.new(0, 2, 0), Geom::Vector3d.new(1, 0, 0)]
line2 = [Geom::Point3d.new(3, 0, 0), Geom::Vector3d.new(0, 1, 0)]
# This will return a point Point3d(3, 2, 0).
points = Geom.closest_points(line1, line2)

Parameters:

Returns:

Version:

  • SketchUp 6.0

.fit_plane_to_points(point1, point2, point3, ...) ⇒ Array(Geom::Point3d, Geom::Vector3d) .fit_plane_to_points(points) ⇒ Array(Geom::Point3d, Geom::Vector3d)

The fit_plane_to_points method is used to compute a plane that is a best fit to an array of points. If more than three points are given some of the points may not be on the plane.

The plane is returned as an Array of 4 numbers which are the coefficients of the plane equation Ax + By + Cz + D = 0.

Examples:

point1 = Geom::Point3d.new(0, 0, 0)
point2 = Geom::Point3d.new(10, 10, 10)
point3 = Geom::Point3d.new(25, 25, 25)
plane = Geom.fit_plane_to_points(point1, point2, point3)

Overloads:

Version:

  • SketchUp 6.0

.intersect_line_line(line1, line2) ⇒ Geom::Point3d?

The intersect_line_line computes the intersection of two lines.

Examples:

# Defines a line parallel to the Y axis, offset 20 units.
line1 = [Geom::Point3d.new(20, 0, 0), Geom::Vector3d.new(0, 1, 0)]
# Defines a line parallel to the X axis, offset 10 units.
line2 = [Geom::Point3d.new(0, 10, 0), Geom::Point3d.new(20, 10, 0)]
# This will return a point Point3d(20, 10, 0).
point = Geom.intersect_line_line(line1, line2)

Parameters:

Returns:

  • (Geom::Point3d, nil)

    The intersection point. Returns nil if they do not intersect.

See Also:

Version:

  • SketchUp 6.0

.intersect_line_plane(line, plane) ⇒ Geom::Point3d?

The intersect_line_plane method is used to compute the intersection of a line and a plane.

Examples:

# Defines a line parallel to the X axis, offset 20 units.
line = [Geom::Point3d.new(-10, 20, 0), Geom::Vector3d.new(1, 0, 0)]
# Defines a plane with it's normal parallel to the x axis.
plane = [Geom::Point3d.new(10, 0 ,0), Geom::Vector3d.new(1, 0, 0)]
# This will return a point Point3d(10, 20, 0).
point = Geom.intersect_line_plane(line, plane)

Parameters:

Returns:

  • (Geom::Point3d, nil)

    A Point3d object. Returns nil if they do not intersect.

See Also:

Version:

  • SketchUp 6.0

.intersect_plane_plane(plane1, plane2) ⇒ Array(Geom::Point3d, Geom::Vector3d)

The intersect_plane_plane method is used to compute the intersection of two planes.

Examples:

# Defines a plane with it's normal parallel to the x axis.
plane1 = [Geom::Point3d.new(10, 0 ,0), Geom::Vector3d.new(1, 0, 0)]
# Defines a plane with it's normal parallel to the y axis.
plane2 = [Geom::Point3d.new(0, 20 ,0), Geom::Vector3d.new(0, 1, 0)]
# This will return a line [Point3d(10, 20, 0), Vector3d(0, 0, 1)].
line = Geom.intersect_plane_plane(plane1, plane2)

Parameters:

Returns:

Version:

  • SketchUp 6.0

.linear_combination(weight1, point1, weight2, point2) ⇒ Geom::Point3d .linear_combination(weight1, vector1, weight2, vector2) ⇒ Geom::Vector3d

The linear_combination method is used to compute the linear combination of points or vectors.

Examples:

point1 = Geom::Point3d.new(1, 1, 1)
point2 = Geom::Point3d.new(10, 10, 10)
# Gets the point on the line segment connecting point1 and point2 that is
# 3/4 the way from point1 to point2: Point3d(7.75, 7.75, 7.75).
point = Geom.linear_combination(0.25, point1, 0.75, point2)

Overloads:

Version:

  • SketchUp 6.0

.point_in_polygon_2D(point, *polygon, check_border) ⇒ Boolean

The point_in_polygon_2D method is used to determine whether a point is inside a polygon. The z component of both the point you're checking and the points in the polygon are ignored, effectively making it a 2-d check.

Examples:

# Create a point that we want to check. (Note that the 3rd coordinate,
# the z, is ignored for purposes of the check.)
point = Geom::Point3d.new(5, 0, 10)

# Create a series of points of a triangle we want to check against.
triangle = []
triangle << Geom::Point3d.new(0, 0, 0)
triangle << Geom::Point3d.new(10, 0, 0)
triangle << Geom::Point3d.new(0, 10, 0)

# Test to see if our point is inside the triangle, counting hits on
# the border as an intersection in this case.
hits_on_border_count = true
status = Geom.point_in_polygon_2D(point, triangle, hits_on_border_count)

Parameters:

  • point (Geom::Point3d)
  • polygon (Array<Geom::Point3d>)

    An array of points that represent the corners of the polygon you are checking against.

  • check_border (Boolean)

    Pass true if a point on the border should be counted as inside the polygon.

Returns:

  • (Boolean)

    true if the point is inside the polygon.

Version:

  • SketchUp 6.0