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.

Return type:: Vec2

GetDirection()¶

Returns the normalized direction vector. Also available as direction.

Return type:: Vec2

direction¶

origin¶

class Rectangle2¶

class Rectangle2(top_left, bottom_right)

Axis aligned rectangle. The first signature creates a rectangle with top-left corner (-1, -1) and bottom-right corner (1, 1), wheras the second method allows to set the top-left and bottom-right corners directly.

Parameters:

top_left (Vec2) – The top-left corner
bottom_right (Vec2) – The bottom-right corner

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

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

width¶

Type:: float

height¶

Type:: float

GetStart()¶

Get top-left corner

Return type:: Vec2

GetEnd()¶

Get bottom-right corner

Return type:: Vec2

SetStart(top_left)¶: Set top-left corner, leaving the bottom-right corner untouched.

SetEnd(bottom_right)¶: Set the bottom-right corner, leaving the top-left 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 x-axis.

At(t)¶: ?

AtAngle(angle)¶: ?

GetBoundingBox()¶

Returns the bounding rectangle (axis-aligned) of the ellipse

Return type:: Rectangle2

GetA()¶: Returns the first principal-axis

GetB()¶: Returns the second principal-axis

GetGamma()¶: Returns the angle of the first principal axis to the x-axis

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 x-axis

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.

Return type:: Vec3

GetDirection()¶

Returns the normalized direction vector. Also available as direction.

Return type:: Vec3

direction¶

Type:: Vec3

origin¶

Type:: Vec3

class Plane¶

class Plane(p1, p2, p3)

class Plane(x, y, z, p)

class Plane(line, point)

class Plane(point, normal)

A plane in 3d-space. 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

Return type:: Vec3

GetP()¶

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

Return type:: float

GetOrigin()¶

Get the origin of the plane. Also available as origin.

Return type:: Vec3

origin¶

Type:: Vec3

normal¶

Type:: Vec3

p¶

Type:: float

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. Read-write. Also available as GetRadius(), SetRadius().

Type:: float

origin¶

The center of the sphere. Read-write. Also available as GetOrigin(), SetOrigin().

Type:: Vec3

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

Return type:: Vec3

GetMax()¶

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

Return type:: Vec3

class CuboidAxis¶

class CuboidAxis(dir, half_extent)

A cuboid axis is defined by a half-extent, 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()

Type:: Vec3

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()

Type:: float

extent¶

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

Type:: float

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 right-handed coordinate system. If a right-handed 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)

Parameters:

center (Vec3) – The center
axis_a (CuboidAxis) – The first axis
axis_b (CuboidAxis) – The second axis
axis_c (CuboidAxis) – The third axis

center¶

The center of the cuboid.

Type:: Vec3

axis_a¶

The first cuboid axis

Type:: CuboidAxis

axis_b¶

The second cuboid axis

Type:: CuboidAxis

axis_c¶

The third cuboid axis

Type:: CuboidAxis

Operations on Geometrical Objects¶

Angle(lhs, rhs)¶

Calculate the angle (in radians) between lhs and rhs.

Parameters:

lhs (Line2, Line3, Plane) – First object
rhs (Line2, Line3, Plane) – Second object

Return type:

float

IntersectionPoint(lhs, rhs)¶

Calculates and returns the intersection point between lhs and rhs

Parameters:

lhs (Line2, Line3, Plane) – First object
rhs (Line2, Line3, Plane) – Second object

Raises:

RuntimeError when the two objects do not intersect

Return type:

Vec3 (Vec2 in case of Line2)

IntersectionLine(plane1, 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:

lhs (Line2, Line3, Plane) – First object
rhs (Line2, Line3, Plane) – Second object

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.

Return type:: bool

IsInPlane(plane, object, epsilon=geom.EPSILON)¶

Check whether object lies in plane and returns true if the difference is no bigger than epsilon.

Parameters:

plane (Plane) – The plane
object (Vec3 or Line3) – The object

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:

lhs (Line2, Line3, Plane) – First object
rhs (Line2, Line3, Plane) – Second object

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:

lhs (Line2, Line3) – First line
rhs (Line2, Line3) – Second line

Return type:

bool

IsInSphere(sphere, point)¶

Check whether the sphere contains point.

Return type:: bool

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

Geometric Objects¶

Geometrical Objects in Two Dimensions¶

Geometrical Objects in Three Dimensions¶

Operations on Geometrical Objects¶

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