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:	`GeomException` 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:	:exc:GeomException 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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