Package rst.geometry

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

This package contains data types which represent geometrical objects.

See also

Wikipedia article containing the definition above

http://en.wikipedia.org/wiki/Geometry

See also

Corresponding data types in ROS

http://www.ros.org/wiki/geometry_msgs

Messages

• BoundingBox3DFloatSet
• PointPair
• Shape3DFloat
• ViewFrustum
• Lengths
• CameraPose
• Cylinder3DFloatSet
• Cylinder3DFloat
• PointCloudSet3DFloat
• PointCloud3DFloat
• BoundingBox3DFloat
• Pose
• Rotation
• AxisAlignedBoundingBox3DFloat
• Translation
• FieldOfView
• BoundingBox

clearer: should be made invisible via css

Message BoundingBox3DFloatSet

class rst.geometry.BoundingBox3DFloatSet

A set of BoundingBox3DFloat objects.

Code author: Christian Emmerich <cemmeric@cor-lab.de>

boxes

Type :array of rst.geometry.BoundingBox3DFloat

Empty collection of boxes is allowed. The order of box objects is not significant.

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message BoundingBox3DFloatSet {

    /**
     * Empty collection of boxes is allowed.
     * The order of box objects is not significant.
     */
    repeated geometry.BoundingBox3DFloat boxes = 1;

}

Message PointPair

class rst.geometry.PointPair

A message representing a pair of 2D Points

Code author: TODO

first

Type :rst.math.Vec2DFloat

TODO

second

Type :rst.math.Vec2DFloat

TODO

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message PointPair {

    /**
     * TODO
     */
    required math.Vec2DFloat first = 1;

    /**
     * TODO
     */
    required math.Vec2DFloat second = 2;

}

Message Shape3DFloat

class rst.geometry.Shape3DFloat

Description of a 3D shape as a union of geometric primitives.

New primitive types can be added to this type.

Code author: Johannes Wienke <jwienke@techfak.uni-bielefeld.de>

Code author: Jan Moringen <jmoringe@techfak.uni-bielefeld.de>

box

Type :array of rst.geometry.BoundingBox3DFloat

Set of oriented bounding boxes contributing to the described 3D shape.

The order of bounding boxes is not significant.

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message Shape3DFloat {

    /**
     * Set of oriented bounding boxes contributing to the described 3D
     * shape.
     *
     * The order of bounding boxes is not significant.
     */
    repeated geometry.BoundingBox3DFloat box = 1;

}

Message ViewFrustum

class rst.geometry.ViewFrustum

Constraint: .maximal_distance > .minimal_distance

A camera’s view frustum.

Adds information about the maximal and minimal perceivable distance (minimal_distance, maximal_distance) of a sensor to the definition of its field of view (fov).

Code author: Leon Ziegler <lziegler@techfak.uni-bielefeld.de>

fov

Type :rst.geometry.FieldOfView

The field of view of the frustum.

minimal_distance

Type :FLOAT32

Constraint: value > 0

Unit: meter

The minimal perceivable distance.

maximal_distance

Type :FLOAT32

Constraint: value > 0

Unit: meter

The maximal perceivable distance.

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message ViewFrustum {

    /**
     * The field of view of the frustum.
     */
    required FieldOfView fov = 1;

    /**
     * The minimal perceivable distance.
     */
    // @constraint(value > 0)
    // @unit(meter)
    optional float minimal_distance = 2 [default = 0];

    /**
     * The maximal perceivable distance.
     */
    // @constraint(value > 0)
    // @unit(meter)
    optional float maximal_distance = 3 [default = 99999];

}

Message Lengths

class rst.geometry.Lengths

A sequence of length measurements (e.g. length of a link in a kinematics chain).

Code author: Arne Nordmann <anordman@techfak.uni-bielefeld.de>

lengths

Type :array of FLOAT64

Unit: meter

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message Lengths {

    // @unit(meter)
    repeated double lengths = 1;

}

Message CameraPose

class rst.geometry.CameraPose

Pose of a camera with semantic annotation of the axes.

The pure transformation of the camera’s pose (in terms of coordinate systems) does not provide information about the viewing direction. There must be a convention about the semantic meaning of the transformation in order to convey the information about where the camera actually looks. coordinate_frame realizes this convention by describing the three axes of the camera’s coordinate system semantically including viewing direction and up direction.

Code author: Leon Ziegler <lziegler@techfak.uni-bielefeld.de>

coordinate_frame

Type :rst.geometry.CameraPose.CoordinateFrame

Annotation of the axes.

pose

Type :rst.geometry.Pose

The pose of the camera’s coordinate system in 3d space relative to a given parent coordinate system.

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message CameraPose {

    /**
     * Semantic annotation of the axes. (all right-handed)
     */
    enum CoordinateFrame {

        /**
         * X: right - Y: down - Z: forward (depth axis)
         */
        CAMERA_IMAGE_FRAME = 0;

        /**
         * X: up - Y: right - Z: forward (depth axis)
         */
        CAMERA_X_UP_FRAME = 1;

        /**
         * X: left - Y: up - Z: forward (depth axis)
         */
        CAMERA_Y_UP_FRAME = 2;

        /**
         * X: forward (depth axis) - Y: left - Z: up
         */
        LASER_FRAME = 3;

        /**
         * X: right - Y: up - Z: towards viewer (negative depth axis)
         */
        SCREEN_FRAME = 4;

    }

    /**
     * Annotation of the axes.
     */
    optional CoordinateFrame coordinate_frame = 1 [default = CAMERA_IMAGE_FRAME];

    /**
     * The pose of the camera's coordinate system in 3d space relative
     * to a given parent coordinate system.
     */
    required geometry.Pose pose = 2;

}

Message CoordinateFrame

class rst.geometry.CameraPose.CoordinateFrame

Semantic annotation of the axes. (all right-handed)

CAMERA_IMAGE_FRAME

= 0

X: right - Y: down - Z: forward (depth axis)

CAMERA_X_UP_FRAME

= 1

X: up - Y: right - Z: forward (depth axis)

CAMERA_Y_UP_FRAME

= 2

X: left - Y: up - Z: forward (depth axis)

LASER_FRAME

= 3

X: forward (depth axis) - Y: left - Z: up

SCREEN_FRAME

= 4

X: right - Y: up - Z: towards viewer (negative depth axis)

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    enum CoordinateFrame {

        /**
         * X: right - Y: down - Z: forward (depth axis)
         */
        CAMERA_IMAGE_FRAME = 0;

        /**
         * X: up - Y: right - Z: forward (depth axis)
         */
        CAMERA_X_UP_FRAME = 1;

        /**
         * X: left - Y: up - Z: forward (depth axis)
         */
        CAMERA_Y_UP_FRAME = 2;

        /**
         * X: forward (depth axis) - Y: left - Z: up
         */
        LASER_FRAME = 3;

        /**
         * X: right - Y: up - Z: towards viewer (negative depth axis)
         */
        SCREEN_FRAME = 4;

    }

Message Cylinder3DFloatSet

class rst.geometry.Cylinder3DFloatSet

A set of Cylinder3DFloat objects.

Code author: Christian Emmerich <cemmeric@cor-lab.de>

cylinders

Type :array of rst.geometry.Cylinder3DFloat

Empty collection of cylinders is allowed. The order of cylinders is not significant.

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message Cylinder3DFloatSet {

    /**
     * Empty collection of cylinders is allowed.
     * The order of cylinders is not significant.
     */
    repeated geometry.Cylinder3DFloat cylinders = 1;

}

Message Cylinder3DFloat

class rst.geometry.Cylinder3DFloat

Cylinder in 3D in general position and orientation.

The general cylinder with dimensions radius and height is constructed by translating and rotating (via transformation) a zero-centered, z-oriented axis-aligned cylinder such as below around its center of mass.

                    < radius >
         .---------------------.
        /                       \
      /                           \
     +              +              +  ^
     |\                           /|
     | \                        /  |
     |   `---------------------'   |
     |                             |
     |            Z ^              |
     |              |  ^  Y        |  height
     |              | /            |
     |              |/             |
     |              +-----> X      |
     |                             |
˙    |                             |
     |                             |
     |                             |
     +                             +  v
      \                           /
        \                       /
         `---------------------'

Code author: Christian Emmerich <cemmeric@cor-lab.de>

transformation

Type :rst.geometry.Pose

Transformation, consisting of translation and orientation, of the center of mass of the cylinder.

radius

Type :FLOAT32

Unit: meter

The radius of the cylinder.

height

Type :FLOAT32

Unit: meter

The height of the cylinder.

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message Cylinder3DFloat {

    /**
     * Transformation, consisting of translation and orientation, of
     * the center of mass of the cylinder.
     */
    required geometry.Pose transformation = 1;

    /**
     * The radius of the cylinder.
     */
    // @unit(meter)
    required float radius = 2;

    /**
     * The height of the cylinder.
     */
    // @unit(meter)
    required float height = 3;

}

Message PointCloudSet3DFloat

class rst.geometry.PointCloudSet3DFloat

A set of 3D Point clouds.

Code author: Christian Emmerich <cemmeric@cor-lab.de>

clouds

Type :array of rst.geometry.PointCloud3DFloat

Empty collection of clouds is allowed. The order of cloud objects is not significant.

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message PointCloudSet3DFloat {

    /**
     * Empty collection of clouds is allowed.
     * The order of cloud objects is not significant.
     */
    repeated geometry.PointCloud3DFloat clouds = 1;

}

Message PointCloud3DFloat

class rst.geometry.PointCloud3DFloat

A collection of points in 3D space.

Code author: Jordi Sanchez Riera <jordi.sanchez-riera@inrialpes.fr>

Todo

correct author?

points

Type :array of rst.math.Vec3DFloat

TODO @unit(meter?)

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message PointCloud3DFloat {

    /**
     * TODO
     */
    // @unit(meter?)
    repeated math.Vec3DFloat points = 1;

}

Message BoundingBox3DFloat

class rst.geometry.BoundingBox3DFloat

Bounding-box in 3D in general position and orientation.

The general bounding-box with dimensions width x depth x height is constructed by translating and rotating (via transformation) an axis-aligned bounding-box around its center of mass.

For an axis-aligned version, see AxisAlignedBoundingBox3DFloat.

Code author: Christian Emmerich <cemmeric@cor-lab.de>

Code author: Jan Moringen <jmoringe@techfak.uni-bielefeld.de>

transformation

Type :rst.geometry.Pose

Transformation, consisting of translation and orientation, of the center of mass of the bounding-box.

width

Type :FLOAT32

Unit: meter

The width (along the X axis) of the box.

depth

Type :FLOAT32

Unit: meter

The depth (along the Y axis) of the box.

height

Type :FLOAT32

Unit: meter

The height (along the Z axis) of the box.

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message BoundingBox3DFloat {

    /**
     * Transformation, consisting of translation and orientation, of
     * the center of mass of the bounding-box.
     */
    required geometry.Pose transformation = 1;

    /**
     * The width (along the X axis) of the box.
     */
    // @unit(meter)
    required float width = 2;

    /**
     * The depth (along the Y axis) of the box.
     */
    // @unit(meter)
    required float depth = 3;

    /**
     * The height (along the Z axis) of the box.
     */
    // @unit(meter)
    required float height = 4;

}

Message Pose

class rst.geometry.Pose

Pose data (camera, robot, ...).

Todo

extend explanation

Code author: Arne Nordmann <anordman@techfak.uni-bielefeld.de>

translation

Type :rst.geometry.Translation

TODO

rotation

Type :rst.geometry.Rotation

TODO

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message Pose {

    /**
     * TODO
     */
    required Translation translation = 1;

    /**
     * TODO
     */
    required Rotation rotation = 2;

}

Message Rotation

class rst.geometry.Rotation

Cartesian 3-dimensional rotatory displacement or orientation.

The displacement or orientation (orientation being a rotation from an origin) is in world coordinates and expressed as unit quaternion (all-zero quaternion denotes an invalid orientation/rotation).

Code author: Arne Nordmann <anordman@cor-lab.uni-bielefeld.de>

qw

Type :FLOAT64

TODO

qx

Type :FLOAT64

TODO

qy

Type :FLOAT64

TODO

qz

Type :FLOAT64

TODO

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message Rotation {

    /**
     * TODO
     */
    required double qw = 4;

    /**
     * TODO
     */
    required double qx = 5;

    /**
     * TODO
     */
    required double qy = 6;

    /**
     * TODO
     */
    required double qz = 7;

}

Message AxisAlignedBoundingBox3DFloat

class rst.geometry.AxisAlignedBoundingBox3DFloat

An axis-aligned bounding-box in 3D.

The bounding-box is constructed by spanning at left_front_bottom a rectangular volume of lengths width x depth x height along the positive directions of the X, Y and Z axis respectively.

^ Z
|
|            +----------------------+ ^
|           /                      /|
|          /                      / |
|         /                      /  | height
|        +----------------------+   |
|        |                      |   |
|        |                      |   + v
|     Y  |                      |  / ^
|     ^  |                      | / depth
|    /   |                      |/
|   /    +----------------------+ v
|  /     left_front_bottom
| /      <     width      >
|/
+-----------------------------> X

For a bouding-box in general orientation (i.e. not axis-aligned) see BoundingBox3DFloat.

Code author: Christian Emmerich <cemmeric@cor-lab.de>

Code author: Jan Moringen <jmoringe@techfak.uni-bielefeld.de>

left_front_bottom

Type :rst.geometry.Translation

Coordinates of the bottom left front corner.

width

Type :FLOAT32

Unit: meter

The width (along the X axis) of the box.

depth

Type :FLOAT32

Unit: meter

The depth (along the Y axis) of the box.

height

Type :FLOAT32

Unit: meter

The height (along the Z axis) of the box.

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message AxisAlignedBoundingBox3DFloat {

    /**
     * Coordinates of the bottom left front corner.
     */
    required geometry.Translation left_front_bottom = 1;

    /**
     * The width (along the X axis) of the box.
     */
    // @unit(meter)
    required float width = 2;

    /**
     * The depth (along the Y axis) of the box.
     */
    // @unit(meter)
    required float depth = 3;

    /**
     * The height (along the Z axis) of the box.
     */
    // @unit(meter)
    required float height = 4;

}

Message Translation

class rst.geometry.Translation

Cartesian 3-dimensional translatory displacement or position.

The displacement or position (position being translation from an origin) is expressed in world coordinates.

Code author: Arne Nordmann <anordman@cor-lab.uni-bielefeld.de>

x

Type :FLOAT64

Unit: meter

Cartesian displacement along the x axis

y

Type :FLOAT64

Unit: meter

Cartesian displacement along the y axis

z

Type :FLOAT64

Unit: meter

Cartesian displacement along the z axis

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message Translation {

    /**
     * Cartesian displacement along the x axis
     */
    // @unit(meter)
    required double x = 1;

    /**
     * Cartesian displacement along the y axis
     */
    // @unit(meter)
    required double y = 2;

    /**
     * Cartesian displacement along the z axis
     */
    // @unit(meter)
    required double z = 3;

}

Message FieldOfView

class rst.geometry.FieldOfView

The field of view of a sensor.

The sensor’s FOV is defined as the angular extent of a scene that is imaged by a visual sensor. The outermost observable ray that falls in a sensor’s FOV has the angular distance +/- AOV/2.0 from the optical axis in the respective extent (vertical/horizontal). The angles are given in radian.

Code author: Leon Ziegler <lziegler@techfak.uni-bielefeld.de>

horizontal_aov

Type :FLOAT32

Constraint: value > 0

Unit: radian

An angle defining the horizontal bounds of the FOV.

vertical_aov

Type :FLOAT32

Constraint: value > 0

Unit: radian

An angle defining the vertical bounds of the FOV.

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message FieldOfView {

    /**
     * An angle defining the horizontal bounds of the FOV.
     */
    // @constraint(value > 0)
    // @unit(radian)
    required float horizontal_aov = 1;

    /**
     * An angle defining the vertical bounds of the FOV.
     */
    // @constraint(value > 0)
    // @unit(radian)
    required float vertical_aov = 2;

}

Message BoundingBox

class rst.geometry.BoundingBox

Constraint: .top_left.x < .image_width

Constraint: .top_left.x + .width <= .image_width

Constraint: .top_left.y < .image_height

Constraint: .top_left.y + .height <= .image_height

A bounding box, which is associated to a raster image.

(0,0)           Image
+----------------------------------+ ^
|                                  |
|    top_left                    |
|    +---------------+ ^           |
|    |               |             |
|    |               | height    | image_height
|    |               |             |
|    +---------------+ v           |
|    <    width     >            |
|                                  |
+----------------------------------+ v
<         image_width            >

All values are in pixels and refer to the associated image.

Code author: Johannes Wienke <jwienke@techfak.uni-bielefeld.de>

top_left

Type :rst.math.Vec2DInt

Unit: pixel

Coordinates of the top left corner.

width

Type :UINT32

Unit: pixel

Width of the bounding box.

height

Type :UINT32

Unit: pixel

Height of the bounding box.

image_width

Type :UINT32

Unit: pixel

Width of the image the bounding box is based on.

image_height

Type :UINT32

Unit: pixel

Height of the image the bounding box is based on.

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message BoundingBox {

    /**
     * Coordinates of the top left corner.
     */
    // @unit(pixel)
    required math.Vec2DInt top_left = 1;

    /**
     * Width of the bounding box.
     */
    // @unit(pixel)
    required uint32 width = 2;

    /**
     * Height of the bounding box.
     */
    // @unit(pixel)
    required uint32 height = 3;

    /**
     * Width of the image the bounding box is based on.
     */
    // @unit(pixel)
    optional uint32 image_width = 4;

    /**
     * Height of the image the bounding box is based on.
     */
    // @unit(pixel)
    optional uint32 image_height = 5;

}