Geom module

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.
 
A line can be represented as either an Array of a point and a vector, or as an Array of two points.
line = [Geom::Point3d.new(0,0,0), Geom::Vector3d.new(0,0,1)]
line = [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 given the coeficients of a plane equation.
plane = [Geom::Point3d.new(0,0,0), Geom::Vector3d.new(0,0,1)]
plane = [0,0,1,0]
 
NOTE:  Lines and Planes are infinite.
 
There are several good books on 3D math if you are new to the concepts of a line, plane, and vector.

Parent: N/A

Methods: closest_points, fit_plane_to_points, intersect_line_line, intersect_line_plane, intersect_plane_plane, linear_combination, point_in_polygon_2d

Example Code: geomtests.rb 

Module Methods

closest_points

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

Syntax

pts = Geom.closest_points line1, line2 
  

Return Value

pts - an array of two points. The first point is on the first line and the second point is on the second line.

Example

line1 = [Geom::Point3d.new(0,0,0), Geom::Vector3d.new(0,0,1)]
line2 = [Geom::Point3d.new(0,0,0), Geom::Vector3d.new(0,0,100)]
# 0,0,0 on each line should be closest because both lines start from
# that point
pts = Geom.closest_points line1, line2

fit_plane_to_points 

The fit_plane_to_points method is used to compute a plane that is a best fit to an array of points

Syntax

plane = Geom.fit_plane_to_points points

plane = Geom.fit_plane_to_points point1, point2, point3, ...

Arguments

points - an array of points

point1, point2, point3 - Point3D objects

Return Value

plane - a plane

Comments

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

intersect_line_line 

The intersect_line_line computes the intersection of two lines.

Syntax

point = Geom.intersect_line_line line1, line2 

Arguments

line1, line2 - A line is given as either an array of a point and a vector, or an Array or two points.

Return Value

Returns nil if they do not intersect.

Example

line1=[Geom::Point3d.new(10,0,0),Geom::Vector3d.new(1,0,0)]
line2=[Geom::Point3d.new(0,10,0),Geom::Point3d.new(20,10,0)] 
pt = Geom.intersect_line_line(line1, line2) 
This will return the point (10,10,0). 

intersect_line_plane 

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

Syntax

point = Geom.intersect_line_plane line, plane 

Arguments

line - a line

plane - a plane

Return Value

point - a Point3d object

Example

# This is really the normal which follows the x axis. The plane is
# perpendicular
plane1 = [Geom::Point3d.new(-10, 0 ,0), Geom::Vector3d.new(1,0,0)]
# This line follows the x axis
line1 = [Geom::Point3d.new(-10,0,0), Geom::Vector3d.new(1,0,0)]
# returns -10, 0, 0
pt = Geom.intersect_line_plane(line1, plane1)

intersect_plane_plane 

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

Syntax

line = Geom.intersect_plane_plane plane1, plane2 

Arguments

plane1, plane2 - planes

Return Value

line - a line where the planes intersect if successful. Returns nil if the planes do not intersect.

Example

# This is really the normal which follows the x axis. The plane is
# perpendicular (or parallel to the Y axis)
plane1 = [Geom::Point3d.new(-10, 0 ,0), Geom::Vector3d.new(1,0,0)]
# This is really the normal which follows the y axis. The plane is
# perpendicular (or parallel to the X axis)
plane2 = [Geom::Point3d.new(0,-10,0), Geom::Vector3d.new(0,1,0)]
# returns (-10,-10,0")(0.0,0.0,1.0)
line = Geom.intersect_plane_plane(plane1, plane2)

linear_combination 

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

Syntax

point = Geom.linear_combination(weight1, point1, weight2, point2)

vector = Geom.linear_combination(weight1, vector1, weight2, vector2)

Arguments

weight1 - a weight or percentage

point1 - the start point on the line

weight2 - a weight or percentage

point2 - the end point of the line

vector1 - the first vector

vector2 - the end point of the line

Return Value

point - point - a Point3d object

vector - vector - a Vector3d object

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.
point = Geom.linear_combination 0.25, point1, 0.75, point2

point_in_polygon_2D 

The point_to_polygon_2D method is used to determine whether a point is inside a polygon when that point is projected as though it and the polygon were in 2D space. The Z component is ignored.

Syntax

status = Geom.point_to_polygon_2D point, points, 
  

Arguments

point - a Point3d object

points - an array of points that represent the points of the polygon you are checking

border - true if a point on the border is counted as inside the polygon.

Return Value

status - true if the point is inside the polygon. False if the point is not inside the polygon.