module Geom
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.
@note Lines and Planes are infinite.
@version SketchUp 6.0
Public Class Methods
The {.closest_points} method is used to compute the closest points on two lines.
line.
@example
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)
@param [Array(Geom::Point3d
, Geom::Vector3d
)] line1
The first line to intersect
@param [Array(Geom::Point3d
, Geom::Vector3d
)] line2
The second line to intersect
@return [Array(Geom::Point3d
, Geom::Point3d
)] An array of two points. The
first point is on the first line and the second point is on the second
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 55 def self.closest_points(line1, line2) end
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
.
@example
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)
@overload fit_plane_to_points
(point1, point2, point3, …)
@param [Geom::Point3d] point1 @param [Geom::Point3d] point2 @param [Geom::Point3d] point3 @return [Array(Geom::Point3d, Geom::Vector3d)] A plane
@overload fit_plane_to_points
(points)
@param [Array<Geom::Point3d>] points @return [Array(Geom::Point3d, Geom::Vector3d)] A plane
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 84 def self.fit_plane_to_points(*args) end
The {.intersect_line_line} computes the intersection of two lines.
@example
# 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)
@param [Array(Geom::Point3d
, Geom::Vector3d
)] line1
The first line to intersect.
@param [Array(Geom::Point3d
, Geom::Vector3d
)] line2
The second line to intersect.
@return [Geom::Point3d, nil] The intersection point. Returns nil
if they
do not intersect.
@see Geom
The Geom module for alternative versions of defining a line.
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 112 def self.intersect_line_line(line1, line2) end
The {.intersect_line_plane} method is used to compute the intersection of a line and a plane.
@example
# 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)
@param [Array(Geom::Point3d
, Geom::Vector3d
)] line
@param [Array(Geom::Point3d
, Geom::Point3d
)] plane
@return [Geom::Point3d, nil] A Point3d
object. Returns nil
if they do not
intersect.
@see Geom
The Geom module for alternative versions of defining lines and planes.
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 138 def self.intersect_line_plane(line, plane) end
The {.intersect_plane_plane} method is used to compute the intersection of two planes.
@example
# 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)
@param [Array(Geom::Point3d
, Geom::Point3d
)] plane1
The first plane to intersect
@param [Array(Geom::Point3d
, Geom::Point3d
)] plane2
The second plane to intersect
@return [Array(Geom::Point3d
, Geom::Vector3d
)] A line where the planes
intersect if successful. Returns +nil+ if the planes do not intersect.
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 164 def self.intersect_plane_plane(plane1, plane2) end
The {.linear_combination} method is used to compute the linear combination of points or vectors.
A linear combination is a standard term for vector math. It is defined as vector = weight1 * vector1 + weight2 * vector2.
@example
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)
@overload linear_combination
(weight1, point1, weight2, point2)
@param [Float] weight1 @param [Geom::Point3d] point1 @param [Float] weight2 @param [Geom::Point3d] point2 @return [Geom::Point3d]
@overload linear_combination
(weight1, vector1, weight2, vector2)
@param [Float] weight1 @param [Geom::Vector3d] vector1 @param [Float] weight2 @param [Geom::Vector3d] vector2 @return [Geom::Vector3d]
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 197 def self.linear_combination(weight1, pt_or_vect1, weight2, pt_or_vect2) end
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.
@example
# 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)
@param [Geom::Point3d] point
@param [Array<Geom::Point3d>] polygon
An array of points that represent the corners of the polygon you are checking against.
@param [Boolean] check_border
Pass true if a point on the border should be counted as inside the polygon.
@return [Boolean] true
if the point is inside the polygon.
@version SketchUp 6.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 233 def self.point_in_polygon_2D(point, polygon, check_border) end
Tessellates a polygon, represented as a collection of 3D points. Can include holes by providing collections of points describing the inner loops. This is intended to be used for planar polygons.
Useful to draw concave polygons using {Sketchup::View#draw} or {Sketchup::View#draw2d}.
It can also be useful for importers where the input format describes only the loops for a polygon and you want to work with a collection of triangles.
Polygon with two holes, one empty and one filled:
(See “Drawing a polygon with holes from a custom tool” example)
@example Iterate over each triangle in the returned set
polygon = [ Geom::Point3d.new(0, 0, 0), Geom::Point3d.new(90, 0, 0), Geom::Point3d.new(60, 40, 0), Geom::Point3d.new(90, 90, 0), Geom::Point3d.new(30, 70, 0), ] triangles = Geom.tesselate(polygon) triangles.each_slice(3) { |triangle| # Work with each triangle set... } # Or get an array of triangles: triangles_set = triangles.each_slice(3).to_a
@example Drawing a polygon with holes from a custom tool
class ExampleTool def initialize polygon = [ Geom::Point3d.new(0, 0, 0), Geom::Point3d.new(90, 0, 0), Geom::Point3d.new(60, 40, 0), Geom::Point3d.new(90, 90, 0), Geom::Point3d.new(30, 70, 0), ] # Counter-clockwise order hole1 = [ Geom::Point3d.new(20, 10, 0), Geom::Point3d.new(40, 10, 0), Geom::Point3d.new(45, 25, 0), Geom::Point3d.new(30, 20, 0), Geom::Point3d.new(25, 25, 0), ].reverse # Clockwise order - empty hole hole2 = [ Geom::Point3d.new(30, 40, 0), Geom::Point3d.new(50, 40, 0), Geom::Point3d.new(50, 50, 0), Geom::Point3d.new(30, 50, 0), ].reverse # Counter-clockwise order - filled hole @triangles = Geom.tesselate(polygon, hole1, hole2) end def activate Sketchup.active_model.active_view.invalidate end def onMouseMove(flags, x, y, view) view.invalidate end def getExtents bounds = Geom::BoundingBox.new bounds.add(@triangles) bounds end def draw(view) view.drawing_color = Sketchup::Color.new(192, 0, 0) view.draw(GL_TRIANGLES, @triangles) end end Sketchup.active_model.select_tool(ExampleTool.new)
@note The winding order of the polygons matter. The outer loop should be
in counter-clockwise order. To cut an empty hole the inner loops should be in clockwise order, otherwise they will create a loop filled with triangles.
@note The tesselation is using the same logic as SketchUp its rendering
pipeline. But the exact result is an implementation detail which may change between versions. In particularly the results of degenerate polygons and non-planar polygons is undefined as part of the API contract. Such polygons are for example polygons where all points are colinear, polygons with duplicate points, non-planar polygons.
@note If you want the triangles from an existing {Sketchup::Face} it's better
to use {Sketchup::Face#mesh}.
@param [Array<Geom::Point3d>] polygon_loop_points
@param [Array<Array<Geom::Point3d>>] inner_loop_points
@raise [ArgumentError] if any of the loops contain less than three points.
@raise [RuntimeError] if the tesselator returned an error.
@return [Array<Geom::Point3d>] an array of points with a stride of three
representing a set of triangles.
@see Sketchup::View#draw
@version SketchUp 2020.0
# File lib/sketchup-api-stubs/stubs/geom.rb, line 348 def self.tesselate(polygon_loop_points, *inner_loop_points) end