Shapes

Global shapes

class geometries.sph.shapes.ball.BallShape.BallShape(location, radius)

Shape of a spherical ball

Construction

Arguments:

  • location (Isometry|Point|Vector) – data for the center of the ball - If the input in an Isometry, then the center is the image of the origin by this isometry. - If the input in a Point, then the center is that point. - If the input is a Vector, then the center is the image of this vector by the exponential map at the origin.

  • radius (number) – the radius od the ball

geometries.sph.shapes.ball.BallShape.BallShape.BallShape

Construction

geometries.sph.shapes.ball.BallShape.BallShape.center

type: Point

Center of the ball

geometries.sph.shapes.ball.BallShape.BallShape.isBallShape

type: boolean

Says that the object inherits from Ball

geometries.sph.shapes.ball.BallShape.BallShape.isGlobal

type: boolean

Says whether the shape is global. True if global, false otherwise.

class geometries.sph.shapes.circle.CircleShape.CircleShape(isom, cz, cw, radius)

Cylinder around a circle of the form z = cst and w = cst Used for instance to draw a wireframe version of the Clifford torus

Constructor The cylinder is the image by isom of the cylinder given by the equations z = cz and w = cw The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” circle - the v-coordinate is such that v = 0 correspond to the point in the e_y direction

Arguments:

  • isom (Isometry) – the position of the cylinder

  • cz (number) – value of the z-coordinate

  • cw (number) – value of the w-coordinate

  • radius (number) – the radius of the cylinder around the curve

geometries.sph.shapes.circle.CircleShape.CircleShape.CircleShape

Constructor The cylinder is the image by isom of the cylinder given by the equations z = cz and w = cw The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” circle - the v-coordinate is such that v = 0 correspond to the point in the e_y direction

class geometries.sph.shapes.cliffordTorus.CliffordTorusShape.CliffordTorusShape(location)

Shape of the Clifford torus in the three-sphere… which is also a cylinder of radius pi/2 around a geodesic!

Construction

Arguments:

  • location (Isometry) – data for the center of the torus (not implemented yet)

geometries.sph.shapes.cliffordTorus.CliffordTorusShape.CliffordTorusShape.CliffordTorusShape

Construction

geometries.sph.shapes.cliffordTorus.CliffordTorusShape.CliffordTorusShape.isCliffordTorusShape

type: boolean

Says that the object inherits from Clifford torus

geometries.sph.shapes.cliffordTorus.CliffordTorusShape.CliffordTorusShape.isGlobal

type: boolean

Says whether the shape is global. True if global, false otherwise.

class geometries.sph.shapes.cylinder.CylinderShape.CylinderShape(isom, radius)

Cylinder in spherical geometry.

Constructor The cylinder is the image by isom of the cylinder going through the origin and directed by e_z The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” geodesic - the v-coordinate is such that v = 0 correspond to the point in the e_y direction

Arguments:

  • isom (Isometry) – the position of the cylinder

  • radius (number) – the radius of the cylinder

geometries.sph.shapes.cylinder.CylinderShape.CylinderShape.CylinderShape

Constructor The cylinder is the image by isom of the cylinder going through the origin and directed by e_z The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” geodesic - the v-coordinate is such that v = 0 correspond to the point in the e_y direction

class geometries.sph.shapes.halfSpace.HalfSpaceShape.HalfSpaceShape(location)

Shape of a half space, which is also a ball of radius pi/2 ! The half space is the (image of by the given isometry of the) space {z < 0}

Construction

Arguments:

  • location (Isometry) – location of the half space

geometries.sph.shapes.halfSpace.HalfSpaceShape.HalfSpaceShape.HalfSpaceShape

Construction

geometries.sph.shapes.halfSpace.HalfSpaceShape.HalfSpaceShape.isGlobal

type: boolean

Says whether the shape is global. True if global, false otherwise.

geometries.sph.shapes.halfSpace.HalfSpaceShape.HalfSpaceShape.isHalfSpaceShape

type: boolean

Says that the object inherits from Ball

geometries.sph.shapes.halfSpace.HalfSpaceShape.HalfSpaceShape.normal

type: Point

Center of the ball

Local shapes

class geometries.sph.shapes.localBall.LocalBallShape.LocalBallShape(location, radius)

Shape of a spherical local ball

Construction

Arguments:

  • location (Isometry|Point|Vector) – data for the center of the ball - If the input in an Isometry, then the center is the image of the origin by this isometry. - If the input in a Point, then the center is that point. - If the input is a Vector, then the center is the image of this vector by the exponential map at the origin.

  • radius (number) – the radius od the ball

geometries.sph.shapes.localBall.LocalBallShape.LocalBallShape.LocalBallShape

Construction

geometries.sph.shapes.localBall.LocalBallShape.LocalBallShape.center

type: Point

Center of the ball

geometries.sph.shapes.localBall.LocalBallShape.LocalBallShape.isGlobal

type: boolean

Says whether the shape is global. True if global, false otherwise.

geometries.sph.shapes.localBall.LocalBallShape.LocalBallShape.isLocalBallShape

type: boolean

Says that the object inherits from Ball

class geometries.sph.shapes.localCylinder.LocalCylinderShape.LocalCylinderShape(isom, radius)

Cylinder in spherical geometry.

Constructor The cylinder is the image by isom of the cylinder going through the origin and directed by e_z The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” geodesic - the v-coordinate is such that v = 0 correspond to the point in the e_y direction

Arguments:

  • isom (Isometry) – the position of the cylinder

  • radius (number) – the radius of the cylinder

geometries.sph.shapes.localCylinder.LocalCylinderShape.LocalCylinderShape.LocalCylinderShape

Constructor The cylinder is the image by isom of the cylinder going through the origin and directed by e_z The UV map takes value in [-pi, pi] x [-pi, pi]. It is computed as follows - the u-coordinate is the distance between the origin and the projection of the on the “core” geodesic - the v-coordinate is such that v = 0 correspond to the point in the e_y direction