# Interface MassObject

An object that has mass, position, velocity and a local coordinate system, and can potentially be dragged by the user.

## Body Coordinates

Each MassObject has its own local coordinate system called body coordinates, distinct from world coordinates (also called simulation coordinates). There are methods for converting between body and world coordinates, see bodyToWorld and worldToBody.

When the MassObject is positioned in world coordinates, we specify the location of the center of mass and the rotation around the center of mass. The rotation is with respect to body coordinates. A rotation of `pi/2` would rotate the MassObject 90 degrees counter clockwise from its starting position.

## Drag Points

A MassObject can have one or more drag points specified to which we typically attach a Spring for the user to be able to move the object. See setDragPoints.

See EventHandler and SimController for information about how MassObjects are used for user interface interactions like dragging an object.

## Potential Energy

For simulations where gravity operates in the vertical direction, there are methods here to help calculate the potential energy of a MassObject. See setZeroEnergyLevel, getZeroEnergyLevel, getMinHeight, and EnergyInfo.

interface MassObject {
alignTo(p_body, p_world, opt_angle?): void;
bodyToWorld(p_body): Vector;
bodyToWorldTransform(): AffineTransform;
createCanvasPath(context): void;
getAngle(): number;
getAngularVelocity(): number;
getBottomBody(): number;
getBottomWorld(): number;
getBoundsBody(): DoubleRect;
getBoundsWorld(): DoubleRect;
getCenterOfMass(): Vector;
getCentroidBody(): Vector;
getCentroidWorld(): Vector;
getChanged(): boolean;
getDragPoints(): Vector[];
getExpireTime(): number;
getHeight(): number;
getKineticEnergy(): number;
getLeftBody(): number;
getLeftWorld(): number;
getMass(): number;
getMinHeight(): number;
getName(opt_localized?): string;
getPosition(): Vector;
getRightBody(): number;
getRightWorld(): number;
getTopBody(): number;
getTopWorld(): number;
getVelocity(p_body?): Vector;
getVerticesBody(): Vector[];
getWidth(): number;
getZeroEnergyLevel(): null | number;
isMassObject(): boolean;
momentum(): number[];
nameEquals(name): boolean;
rotateBodyToWorld(v_body): Vector;
rotateWorldToBody(v_world): Vector;
rotationalEnergy(): number;
setAngle(angle): void;
setAngularVelocity(angular_velocity): void;
setCenterOfMass(center): void;
setChanged(): void;
setDragPoints(dragPts): void;
setExpireTime(time): void;
setMass(mass): void;
setMinHeight(minHeight): void;
setPosition(loc_world, angle?): void;
setPositionX(value): void;
setPositionY(value): void;
setVelocity(velocity_world, angular_velocity?): void;
setVelocityX(value): void;
setVelocityY(value): void;
setZeroEnergyLevel(height?): void;
similar(obj, opt_tolerance?): boolean;
toStringShort(): string;
translationalEnergy(): number;
worldToBody(p_world): Vector;
}

## Methods

• Moves this body so that a certain point on this body is aligned to the given world coordinates location; optionally sets the angle of this body by rotating around the center of mass `angle` radians counter-clockwise from the body coordinates orientation.

#### Parameters

• ##### p_body: GenericVector

the point on this body to be aligned to the new `p_world` location, in body coordinates

• ##### p_world: GenericVector

the world coordinates location to move the specified `p_body` point to

• ##### `Optional`opt_angle: number

the angle in radians to rotate this body counter-clockwise from 'body coordinates' orientation; if not specified then leave the angle as is.

#### Throws

if this MassObject is immoveable

• Returns the world coordinates of the given body coordinates point, based on current position of this object.

#### Parameters

• ##### p_body: GenericVector

the point, in body coordinates

#### Returns Vector

the point in world coordinates

• Returns the AffineTransform from body to world coordinates.

#### Returns AffineTransform

the AffineTransform from body to world coordinates.

• Creates the JavaScript Canvas path that represents the shape of this object in the given Canvas context using body coordinates. Note that this calls `CanvasRenderingContext2D.beginPath()` which discards any currently defined path and begins a new one. Also, this concept of 'path' is different from the path of Edges that makes up a Polygon (though the Canvas path is created from those Polygon paths).

#### Parameters

• ##### context: CanvasRenderingContext2D

the CanvasRenderingContext2D to create the path in

#### Returns void

• Returns the counter-clockwise angle of rotation of this body about its center of mass, in radians, relative to 'body coordinates' orientation.

#### Returns number

the counter-clockwise angle of rotation of this body about its center of mass, in radians, relative to 'body coordinates' orientation

• Returns angular velocity of rotation of this body about its center of mass.

#### Returns number

the angular velocity, in radians/second, with positive meaning counter-clockwise rotation about the body's center of mass

• Returns vertical coordinate of bottom-most point of this body, in body coordinates

#### Returns number

vertical coordinate of bottom-most point of this body, in body coordinates

• Returns vertical coordinate of bottom-most point of this body, based on its current position and orientation, in world coordinates. This is approximate when the body has curved edges; because this looks at all the Vertex's of the body, and curved edges have a series of 'decorated' Vertexes on them which don't capture the exact nature of the geometric curve.

#### Returns number

vertical coordinate of bottom-most point of this body, in world coordinates

• Returns rectangle that contains this body in body coordinates.

#### Returns DoubleRect

rectangle that contains this body in body coordinates

• Returns the location of center of mass, in local body coordinates.

#### Returns Vector

the location of center of mass, in local body coordinates.

• Returns the center of the circle to use for proximity testing, in body coords. A circle centered at this location with radius `getCentroidRadius()` should enclose this MassObject. See getCentroidRadius, getCentroidWorld.

#### Returns Vector

the center of the circle to use for proximity testing, in body coords

• Returns the radius of the circle to use for proximity testing. A circle centered at `getCentroidBody()` with this radius should enclose this MassObject. See getCentroidBody, getCentroidWorld.

#### Returns number

the radius of the circle to use for proximity testing.

• Returns the center of the circle to use for proximity testing, in world coords. A circle centered at this location with radius `getCentroidRadius()` should enclose this MassObject. See getCentroidBody, getCentroidRadius.

#### Returns Vector

the center of the circle to use for proximity testing, in world coords

• Returns whether this SimObject has changed, and sets the state to "unchanged".

#### Returns boolean

whether this SimObject has changed

• Returns the locations in body coordinates where a mouse can drag this object

#### Returns Vector[]

the locations in body coordinates where a mouse can drag this object

• Returns the expiration time, when this SimObject should be removed from the SimList. This is intended for temporary SimObjects that illustrate, for example, contact forces or collisions.

#### Returns number

the expiration time, in time frame of the Simulation clock

• Returns the height of this body, when drawn in body coordinates.

#### Returns number

the height of this body.

• Returns kinetic energy of this body

#### Returns number

kinetic energy of this body

• Returns horizontal coordinate of left-most point of this body, in body coordinates

#### Returns number

horizontal coordinate of left-most point of this body, in body coordinates

• Returns vertical coordinate of left-most point of this body, based on its current position and orientation, in world coordinates. This is approximate when the body has curved edges; because this looks at all the Vertex's of the body, and curved edges have a series of 'decorated' Vertexes on them which don't capture the exact nature of the geometric curve.

#### Returns number

vertical coordinate of left-most point of this body, in world coordinates

• Returns the mass of this object.

#### Returns number

the mass of this object

• Returns the minimum height that this body's center of gravity can reach, used for potential energy calculations. Put another way: this is how low the center of gravity of this body can be when resting on the ground, and the ground is at height zero.

#### Returns number

the minimum height this body can reach.

• Name of this SimObject, either the language-independent name for scripting purposes or the localized name for display to user.

The language-independent name should be the same as the English version but capitalized and with spaces and dashes replaced by underscore, see Util.toName, nameEquals.

The name should give an idea of the role of the SimObject in the simulation. This allows us to to treat an object in a special way depending on its name. For example, we might use the name to decide what type of DisplayObject to create to represent the SimObject.

#### Parameters

• ##### `Optional`opt_localized: boolean

`true` means return the localized version of the name; default is `false` which means return the language independent name.

#### Returns string

name of this SimObject

• Returns the position of the center of mass of this object, in world coordinates.

#### Returns Vector

the position of this object, in world coordinates.

• Returns horizontal coordinate of right-most point of this body, in body coordinates

#### Returns number

horizontal coordinate of right-most point of this body, in body coordinates

• Returns vertical coordinate of right-most point of this body, based on its current position and orientation, in world coordinates. This is approximate when the body has curved edges; because this looks at all the Vertex's of the body, and curved edges have a series of 'decorated' Vertexes on them which don't capture the exact nature of the geometric curve.

#### Returns number

vertical coordinate of right-most point of this body, in world coordinates

• Returns vertical coordinate of top-most point of this body, in body coordinates

#### Returns number

vertical coordinate of top-most point of this body, in body coordinates

• Returns vertical coordinate of top-most point of this body, based on its current position and orientation, in world coordinates. This is approximate when the body has curved edges; because this looks at all the Vertex's of the body, and curved edges have a series of 'decorated' Vertexes on them which don't capture the exact nature of the geometric curve.

#### Returns number

vertical coordinate of top-most point of this body, in world coordinates

• Returns velocity of the given point on this object. The point is specified in body coordinates, but the velocity is in world coordinates.

#### Parameters

• ##### `Optional`p_body: GenericVector

the point to find the velocity of, in body coordinates; if undefined, then center of mass is used

#### Returns Vector

the velocity of the given point, in world coordinates

• Returns the locations of vertices that define a bounding area, in body coordinates. The vertices might lie outside of the body: for example a circle could have vertices at corners of a bounding box.

#### Returns Vector[]

locations of the vertices in body coordinates

• Returns the width of this body, when drawn in body coordinates.

#### Returns number

the width of this body.

• Returns the vertical coordinate where the body has zero potential gravitational energy under standard constant gravity when the body's center of mass is at this vertical coordinate.

#### Returns null | number

the vertical world coordinate where this body has zero potential energy; or null to use the default zero energy level

• Returns moment of inertia about center of mass. This measures how much force is needed to rotate the body about the center of mass. Note that this is the number set via setMomentAboutCM multiplied by the mass of the body.

#### Returns number

moment of inertia about center of mass

• Returns the linear and angular momentum of this body. Angular momentum about a fixed point in space is defined as

``````I_cm vw k + r x m v_cm
``````

where:

``````I_cm = moment about center of mass
vw = angular velocity
k = unit z vector,
r = vector from a fixed point to the center of mass (cm)
m = mass
v_cm = velocity of center of mass
``````

cross product in the plane is `(ax,ay,0) x (bx,by,0) = k(ax by - ay bx)` so we get

``````I_cm w + m (rx vy - ry vx)
``````

take the fixed point to be the origin `(0,0)`, so `(rx,ry)` is center of mass.

#### Returns number[]

the momentum of this body as array containing horizontal, vertical and angular momentum in that order.

• Whether this SimObject has the given name, adjusting for transformation to the language-independent form of the name, as is done by Util.toName.

#### Parameters

• ##### name: string

the English or language-independent version of the name

#### Returns boolean

whether this SimObject has the given name (adjusted to language-independent form)

• Rotates a body coordinates vector to its orientation in world coordinates. The vector goes from the origin (0, 0), to the given point in body coordinates. The vector is rotated about the origin by the current angle of this body.

#### Parameters

• ##### v_body: GenericVector

the vector, in body coordinates

#### Returns Vector

the rotated vector in world coordinates.

• Rotates a world coordinates vector to its orientation in body coordinates, the inverse of rotateBodyToWorld method. The vector goes from the origin `(0, 0)`, to the given point in world coordinates. The vector is rotated about the origin by the opposite of the current angle of this body.

#### Parameters

• ##### v_world: GenericVector

the the vector to be rotated, in world coordinates

#### Returns Vector

the rotated vector in body coordinates.

• Returns the rotational energy of this body. Defined to be: `0.5 * momentAboutCM * vw^2` where `vw = ` angular velocity.

#### Returns number

the rotational energy of this body

• Sets the angle in radians of counter-clockwise rotation of this object around its center of mass. Angle zero draws the object in the same orientation as in body coordinates. Angle `Math.PI/2` rotates the body clockwise 90 degrees from its body coordinates orientation.

#### Parameters

• ##### angle: number

the angle in radians to rotate this object counter-clockwise about its center of mass from 'body coordinates' orientation

#### Returns void

• Sets angular velocity of rotation of this body about its center of mass.

#### Parameters

• ##### angular_velocity: number

the angular velocity, in radians/second, with positive meaning counter-clockwise rotation about the body's center of mass

#### Returns void

• Sets location of center of mass, in body coordinates.

#### Parameters

• ##### center: GenericVector

the position of the center of mass, in body coordinates.

#### Returns void

• Sets the locations where a mouse can drag this object, in body coordinates.

#### Parameters

• ##### dragPts: Vector[]

the locations where a mouse can drag this object, in body coordinates

#### Returns void

• Sets the expiration time, when this SimObject should be removed from the SimList. This is intended for temporary SimObjects that illustrate, for example, contact forces or collisions.

#### Parameters

• ##### time: number

the expiration time, in time frame of the Simulation clock

#### Returns void

• Set the mass of this MassObject.

Note that when setting the mass on a MassObject you should also set accordingly the moment of inertia about center of mass, see setMomentAboutCM.

#### Parameters

• ##### mass: number

the mass of this MassObject

#### Returns void

• Sets the minimum height that this body can reach, used for potential energy calculations. That is, how low can the center of gravity of this body go?

#### Parameters

• ##### minHeight: number

the minimum height that this body can reach.

#### Returns void

• Sets the moment of inertia about the center of mass for this body divided by the mass of this body. The moment of inertia, `Icm`, measures how much force is needed to rotate the body about the center of mass. `Icm` depends on the shape of the object and how mass is distributed. For a thin rectangular plate:

``````Icm = mass * (width^2 + height^2) / 12
``````

For a thin circular plate:

``````Icm = mass * radius^2 / 2
``````

Note that momentAboutCM returns the number specified here multiplied by the mass of the body.

#### Parameters

• ##### moment: number

the moment of inertia about the center of mass for this body divided by the mass of this body

#### Returns void

• Moves this body so that the center of mass is at the given world coordinates location; rotates this body counter-clockwise about center of mass from 'body coordinates' orientation by the given angle in radians.

#### Parameters

• ##### loc_world: GenericVector

the location in world coordinates

• ##### `Optional`angle: number

the angle in radians to rotate this body counter-clockwise from 'body coordinates' orientation; if undefined then angle is not changed

#### Returns void

• Moves this body so that the center of mass is at the given world coordinates X (horizontal) location.

#### Parameters

• ##### value: number

the horizontal location in world coordinates

#### Returns void

• Moves this body so that the center of mass is at the given world coordinates Y (vertical) location.

#### Parameters

• ##### value: number

the vertical location in world coordinates

#### Returns void

• Set the linear velocity of this objects's center of mass, and (optional) angular velocity of rotation about the objects's center of mass.

#### Parameters

• ##### velocity_world: GenericVector

the velocity in world coordinates/second

• ##### `Optional`angular_velocity: number

the angular velocity, in radians/second, with positive meaning counter-clockwise rotation about the body's center of mass; if undefined, then angular velocity is not changed

#### Returns void

• Set the linear horizontal velocity of this objects's center of mass.

#### Parameters

• ##### value: number

the horizontal velocity in world coordinates

#### Returns void

• Set the linear vertical velocity of this objects's center of mass.

#### Parameters

• ##### value: number

the vertical velocity in world coordinates

#### Returns void

• Sets the vertical coordinate where the body has zero potential gravitational energy under standard constant gravity when the body's center of mass is at this vertical coordinate.

#### Parameters

• ##### `Optional`height: number

the vertical world coordinate where this body has zero potential energy; `NaN` means to use default level; `undefined` means use the body's current vertical location is used

#### Returns void

• Returns true if the given SimObject is similar to this SimObject for display purposes. SimObjects are similar when they are the same type and nearly the same size and location. Mainly used when showing forces - to avoid adding too many objects to the display. See SimList.getSimilar.

#### Parameters

• ##### obj: SimObject

the SimObject to compare to

• ##### `Optional`opt_tolerance: number

the amount the object components can differ by

#### Returns boolean

true if this SimObject is similar to `obj` for display purposes

• Returns a minimal string representation of this object, usually giving just identity information like the class name and name of the object.

For an object whose main purpose is to represent another Printable object, it is recommended to include the result of calling `toStringShort` on that other object. For example, calling `toStringShort()` on a DisplayShape might return something like this:

``````DisplayShape{polygon:Polygon{'chain3'}}
``````

#### Returns string

a minimal string representation of this object.

• Returns the translational energy of this body. Defined to be: `0.5*mass*(vx^2 + vy^2)` where `vx = ` horizontal velocity, and `vy = ` vertical velocity.

#### Returns number

the translational energy of this body

• Returns the body coordinates of the given world coordinates point, based on current position of this object.

#### Parameters

• ##### p_world: GenericVector

the point, in world coordinates

#### Returns Vector

the point in body coordinates

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