Geometric Objects
Geometrical Objects in Two Dimensions

class
Line2

class
Line2 (from, to)
Parametric line in two dimensions as defined by an origin and a normalized
direction vector. The first constructor creates a line with origin (0,0) and
direction along the x axis. The second signature creates a line originating
from from and pointing towards to.

At (t)
Returns the point on the line at (signed) distance t from origin.
Parameters:  t (float) – free parameter 
Return type:  Vec2 

GetOrigin ()
Returns the origin of the line: Also available as origin .

GetDirection ()
Returns the normalized direction vector. Also available as
direction .

direction

origin

class
Rectangle2

class
Rectangle2 (top_left, bottom_right)
Axis aligned rectangle. The first signature creates a rectangle with topleft
corner (1, 1) and bottomright corner (1, 1), wheras the second method
allows to set the topleft and bottomright corners directly.
Parameters: 
 top_left (
Vec2 ) – The topleft corner
 bottom_right (
Vec2 ) – The bottomright corner


GetWidth ()
Returns the width of the rectangle. Also available as width .

GetHeight ()
Returns the height of the rectangle. Also available as height .

width


height


GetStart ()
Get topleft corner

GetEnd ()
Get bottomright corner

SetStart (top_left)
Set topleft corner, leaving the bottomright corner untouched.

SetEnd (bottom_right)
Set the bottomright corner, leaving the topleft corner untouched.

class
Circle2

class
Circle2 (circle)

class
Circle2 (center, radius)
The first signature creates a circle centered at (0, 0) and radius 1.0. The
second signature creates a circle with the same paramters as circle. The
third signature creates a new circle with given center and radius.

SetCenter (center)
Set center of circle
Parameters:  center (Vec2 ) – The new center 

SetRadius (radius)
Set radius of circle
Parameters:  center – The new radius 

GetCenter ()
Returns the center of the circle

GetRadius ()
Returns the radius of the circle

GetArea ()
Returns the area of the circle

GetCircumference ()
Returns the circumference of the circle

class
Ellipse2

class
Ellipse2 (center, a, b, gamma)
An ellipse is defined by a center, two principal axis and gamma that
defines the angle between the first principal axis an the xaxis.

At (t)
?

AtAngle (angle)
?

GetBoundingBox ()
Returns the bounding rectangle (axisaligned) of the ellipse

GetA ()
Returns the first principalaxis

GetB ()
Returns the second principalaxis

GetGamma ()
Returns the angle of the first principal axis to the xaxis

GetArea ()
Returns the area of the ellipse

GetOrigin ()
Returns the center of the ellipse

SetA (a)
Set the length of the first principal axis

SetB (b)
Set the length of the second principal axis

SetGamma (gamma)
Set the angle of the first principal axis to the xaxis

SetOrigin (ori)
Set the center of the ellipse
Geometrical Objects in Three Dimensions

class
Line3

class
Line3 (from, to)
Parametric line in three dimensions as defined by an origin and a normalized
direction vector. The first constructor creates a line with origin (0,0) and
direction along the x axis. The second signature creates a line originating
from from and pointing towards to.

At (t)
Returns the point on the line at (signed) distance t from origin.
Parameters:  t (float) – free parameter 
Return type:  Vec3 

GetOrigin ()
Returns the origin of the line: Also available as origin .

GetDirection ()
Returns the normalized direction vector. Also available as
direction .

direction


origin


class
Plane

class
Plane (p1, p2, p3)

class
Plane (x, y, z, p)

class
Plane (line, point)

class
Plane (point, normal)
A plane in 3dspace. The plane can be constructed by either passing in 3
points (p1, p2, p3), a normal and a point, the four parameters that define the
implicit plane equation (x, y, z, p) or a line and a point.

GetNormal ()
Returns the normal of the plane. Also available as normal

GetP ()
Returns the plane offset, i.e. the projection of any point on the plane onto
the normal. Also available as p .

GetOrigin ()
Get the origin of the plane. Also available as origin .

origin


normal


p


class
Sphere

class
Sphere (center, radius)
Represents a sphere in 3d space. The first constructor creates a sphere with
radius 1, centered at (0, 0, 0), the second allows you to set the radius and
center directly.
Parameters: 
 center (
Vec3 ) – The center
 radius (float) – The radius


radius
The radius of the sphere. Readwrite. Also available as GetRadius() ,
SetRadius() .

origin
The center of the sphere. Readwrite. Also available as GetOrigin() ,
SetOrigin() .

GetOrigin ()
See origin

SetOrigin (origin)
See origin

GetRadius ()
See radius

SetRadius (radius)
See radius

class
AlignedCuboid (min, max)
Axis aligned cuboid is a cuboid whose axes are aligned to the x, y, and z
axes of the coordinate system. For arbitrarily oriented bounding cuboid
class, see Cuboid .

GetMin ()
Get minimum coordinate, i.e. the lower bound of x, y, and z for
any point in the cuboid

GetMax ()
Get maximum coordinate, i.e. the upper bound of x, y, and z for
any point in the cuboid.

class
CuboidAxis

class
CuboidAxis (dir, half_extent)
A cuboid axis is defined by a halfextent, and a direction vector. This class
is used in together with the Cuboid class.
Parameters: 
 dir (
Vec3 ) – Direction vector, will be normalized
 half_extent (float) – The half extent


vector
The normalized direction vector of the cuboid axis. Also available as
GetVector()

half_extent
The half extent of the cuboid axis is the magnitude of the cuboid
axis measured from the center to the corner. Also available as
GetHalfExtent()

extent
The extent of the cuboid axis. This value is always twice the
half_extent . Readonly. Also available as
GetExtent() .

GetHalfExtent ()
See half_extent

GetExtent ()
See extent

GetVector ()
See vector

class
Cuboid (center, axis_a, axis_b, axis_c)
An arbitrarily oriented cuboid defined by a center and 3 axis. The 3 cuboid
axis are stored in the order they are passed to the constructor. This means,
that there is no guarantee that the 3 axes form a righthanded coordinate
system. If a righthanded coordinate system is a requirement, you have to
ensure this on your own:
center=...
axis_a=geom.CuboidAxis(...)
axis_b=geom.CuboidAxis(...)
axis_c=geom.CuboidAxis(geom.Cross(axis_a.vector, axis_b.vector), ...)
cuboid=geom.Cuboid(center, axis_a, axis_b, axis_c)

center
The center of the cuboid.

axis_a
The first cuboid axis

axis_b
The second cuboid axis

axis_c
The third cuboid axis
Operations on Geometrical Objects

Angle (lhs, rhs)
Calculate the angle (in radians) between lhs and rhs.
Parameters: 

Return type:  float


IntersectionPoint (lhs, rhs)
Calculates and returns the intersection point between lhs and rhs
Parameters: 

Raises:  RuntimeError when the two objects do not intersect

Return type:  Vec3 (Vec2 in case of Line2 )


IntersectionLine (plane2, plane2)
Returns the intersection line between plane1 and plane2.
Parameters: 
 plane1 (
Plane ) – The first plane
 plane2 (
Plane ) – The second plane

Raises:  RuntimeError if the two planes are parallel.


Distance (lhs, rhs)
Returns the minimal distance between lhs and rhs.
Parameters: 

Return type:  float


IsOnLine (line, point, epsilon=geom.EPSILON)
Check whether point lies on line and returns true if point i no further
away than epsilon.

IsInPlane (plane, object, epsilon=geom.EPSILON)
Check whether object lies in plane and returns true if the difference is
no bigger than epsilon.
Parameters: 

Return type:  bool


AreParallel (lhs, rhs, epsilon=geom.EPSILON)
Check whether lhs and rhs are parallel and returns true, if the difference
is below the given treshold epsilon.
Parameters: 

Return type:  bool


AreIntersecting (line1, line2, epsilon=geom.EPSILON)
Check whether line1 and line2 are intersecting and returns true, if they
intersect below the given threshold epsilon.
Parameters: 

Return type:  bool


IsInSphere (sphere, point)
Check whether the sphere contains point.

MinDistance (list1, list2)
Calculate the minimal distance between two sets of points
Parameters: 
 list1 (
Vec3List ) – the first set of points
 list2 (
Vec3List ) – the second set of points


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