Box (Euclid)

Box Type

Namespace: Euclid
Assembly: Euclid.dll
Base Type: ValueType
Kind: Struct

 An immutable 3D Box with any rotation in 3D space.
 Described by an Origin and three Edge vectors.
 Similar to PPlane, however the three vectors are not unitized.
 This implementation guarantees the box to be always valid.
 That means the Min X, Y and Z axes cannot be flipped individually.
 However the length of one of these axes might still be zero.

   local        local
   Z-Axis       Y-Axis
   ^           /
   |   7      /        6
   |   +---------------+
   |  /|    /         /|
   | / |   /         / |
 4 |/  |  /       5 /  |
   +---------------+   |
   |   |/          |   |
   |   +-----------|---+
   |  / 3          |  / 2
   | /             | /
   |/              |/     local
   +---------------+----> X-Axis
   0               1

Record fields

Record Field	Description
`Origin` Full Usage: `Origin` Field type: `Pnt`	The Origin Corner of the Box. Field type: `Pnt`
`Xaxis` Full Usage: `Xaxis` Field type: `Vec`	The Edge vector representing the X-axis of the Box. Field type: `Vec`
`Yaxis` Full Usage: `Yaxis` Field type: `Vec`	The Edge vector representing the Y-axis of the Box. Field type: `Vec`
`Zaxis` Full Usage: `Zaxis` Field type: `Vec`	The Edge vector representing the Z-axis of the Box. Field type: `Vec`

Instance members

Instance member	Description
`this.AreaSq` Full Usage: `this.AreaSq` Returns: `float` Modifiers: inline	Calculates the squared volume of the Box. by using the squared lengths of the X , Y and Z axis. This is a bit faster than calculating the area and good enough for relative comparisons or sorting by size. Returns: `float`
`this.AsString` Full Usage: `this.AsString` Returns: `string`	Format Box into string with nice floating point number formatting of X, Y and Z size only. But without type name as in v.ToString() Returns: `string`
`this.BBox` Full Usage: `this.BBox` Returns: `BBox`	Gets the axis aligned 3D Bounding Box of the Box. Returns: `BBox`
`this.BackFace` Full Usage: `this.BackFace` Returns: `Rect3D`	Returns the back face of the Box in Counter-Clockwise order, looking from front. Returns Origin at point 3, X-Axis to point 2, Y-Axis to point 7. The normal of the Rect3D points into the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.BottomFace` Full Usage: `this.BottomFace` Returns: `Rect3D`	Returns the bottom face of the Box in Counter-Clockwise order, looking from above. Returns Origin at point 0, X-Axis to point 1, Y-Axis to point 3. The normal of the Rect3D points into the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.Center` Full Usage: `this.Center` Returns: `Pnt` Modifiers: inline	The center of the Box. Returns: `Pnt`
`this.Contains` Full Usage: `this.Contains` Parameters: p : `Pnt` Returns: `bool`	Check for point containment in the Box. By doing 6 dot products with the sides of the rectangle. A point exactly on the edge of the Box is considered inside. p : `Pnt` Returns: `bool`
`this.Diagonal` Full Usage: `this.Diagonal` Returns: `Vec` Modifiers: inline	The diagonal vector of the Box. Returns: `Vec`
`this.EvaluateAt` Full Usage: `this.EvaluateAt` Parameters: xParameter : `float` yParameter : `float` zParameter : `float` Returns: `Pnt` Modifiers: inline	Evaluate a X, Y and Z parameter of the Box. 0.0, 0.0, 0.0 returns the Origin. 1.0, 1.0, 1.0 returns the FarCorner. xParameter : `float` yParameter : `float` zParameter : `float` Returns: `Pnt`
`this.FarCorner` Full Usage: `this.FarCorner` Returns: `Pnt` Modifiers: inline	The corner diagonally opposite of corner from Origin. Returns: `Pnt`
`this.FrontFace` Full Usage: `this.FrontFace` Returns: `Rect3D`	Returns the front face of the Box in Counter-Clockwise order, looking from front. Returns Origin at point 0, X-Axis to point 1, Y-Axis to point 4. The normal of the Rect3D points away from the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.LeftFace` Full Usage: `this.LeftFace` Returns: `Rect3D`	Returns the left face of the Box in Counter-Clockwise order, looking from right. Returns Origin at point 0, X-Axis to point 3, Y-Axis to point 4. The normal of the Rect3D points into the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.Plane` Full Usage: `this.Plane` Returns: `PPlane` Modifiers: inline	Gets the Plane that this box is based on. Returns: `PPlane`
`this.Points` Full Usage: `this.Points` Returns: `Pnt[]`	Returns the bottom corners of the Box in Counter-Clockwise order, starting at Origin. Then the top corners staring above Origin. Returns an array of 8 Points. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt[]`
`this.Pt0` Full Usage: `this.Pt0` Returns: `Pnt` Modifiers: inline	Returns point 0 of the box, same box.Origin. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt1` Full Usage: `this.Pt1` Returns: `Pnt` Modifiers: inline	Returns point 1 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt2` Full Usage: `this.Pt2` Returns: `Pnt` Modifiers: inline	Returns point 2 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt3` Full Usage: `this.Pt3` Returns: `Pnt` Modifiers: inline	Returns point 3 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt4` Full Usage: `this.Pt4` Returns: `Pnt` Modifiers: inline	Returns point 4 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt5` Full Usage: `this.Pt5` Returns: `Pnt` Modifiers: inline	Returns point 5 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt6` Full Usage: `this.Pt6` Returns: `Pnt` Modifiers: inline	Returns point 6 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.Pt7` Full Usage: `this.Pt7` Returns: `Pnt` Modifiers: inline	Returns point 7 of the box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Pnt`
`this.RightFace` Full Usage: `this.RightFace` Returns: `Rect3D`	Returns the right face of the Box in Counter-Clockwise order, looking from right. Returns Origin at point 1, X-Axis to point 2, Y-Axis to point 5. The normal of the Rect3D points away from the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.SizeX` Full Usage: `this.SizeX` Returns: `float` Modifiers: inline	The size in X direction. Returns: `float`
`this.SizeXSq` Full Usage: `this.SizeXSq` Returns: `float` Modifiers: inline	The size in X direction squared. Returns: `float`
`this.SizeY` Full Usage: `this.SizeY` Returns: `float` Modifiers: inline	The size in Y direction. Returns: `float`
`this.SizeYSq` Full Usage: `this.SizeYSq` Returns: `float` Modifiers: inline	The size in Y direction squared. Returns: `float`
`this.SizeZ` Full Usage: `this.SizeZ` Returns: `float` Modifiers: inline	The size in Z direction. Returns: `float`
`this.SizeZSq` Full Usage: `this.SizeZSq` Returns: `float` Modifiers: inline	The size in Z direction squared. Returns: `float`
`this.TopFace` Full Usage: `this.TopFace` Returns: `Rect3D`	Returns the top face of the Box in Counter-Clockwise order, looking from above. Returns Origin at point 4, X-Axis to point 5, Y-Axis to point 7. The normal of the Rect3D points away from the Box. local local Z-Axis Y-Axis ^ / \| 7 / 6 \| +---------------+ \| /\| / /\| \| / \| / / \| 4 \|/ \| / 5 / \| +---------------+ \| \| \|/ \| \| \| +-----------\|---+ \| / 3 \| / 2 \| / \| / \|/ \|/ local +---------------+----> X-Axis 0 1 Returns: `Rect3D`
`this.Volume` Full Usage: `this.Volume` Returns: `float` Modifiers: inline	Calculates the volume of the Box. Returns: `float`
`this.XaxisUnit` Full Usage: `this.XaxisUnit` Returns: `Vec` Modifiers: inline	Creates a unitized version of the local X-Axis. Returns: `Vec`
`this.YaxisUnit` Full Usage: `this.YaxisUnit` Returns: `Vec` Modifiers: inline	Creates a unitized version of the local Y-Axis. Returns: `Vec`
`this.ZaxisUnit` Full Usage: `this.ZaxisUnit` Returns: `Vec` Modifiers: inline	Creates a unitized version of the local Z-Axis. Returns: `Vec`

Static members

Static member	Description
`Box.contains p b` Full Usage: `Box.contains p b` Parameters: p : `Pnt` b : `Box` Returns: `bool` Modifiers: inline	Check for point containment in the Box. By doing 6 dot products with the sides of the rectangle. A point exactly on the edge of the Box is considered inside. p : `Pnt` b : `Box` Returns: `bool`
`Box.createFromBoundingBox b` Full Usage: `Box.createFromBoundingBox b` Parameters: b : `BBox` Returns: `Box`	Creates a 3D box from a 3D a bounding box. b : `BBox` Returns: `Box`
`Box.createFromDirsAndPoints dirX dirY pts` Full Usage: `Box.createFromDirsAndPoints dirX dirY pts` Parameters: dirX : `Vec` dirY : `Vec` pts : `IList<Pnt>` Returns: `Box`	Finds the oriented bounding box in 3D of a set of points. The orientation of the X-axis is defined by the dirX vector. The orientation of the Y-axis is defined by the dirY vector. dirX : `Vec` dirY : `Vec` pts : `IList<Pnt>` Returns: `Box`
`Box.createFromPlane (pl, x, y, z)` Full Usage: `Box.createFromPlane (pl, x, y, z)` Parameters: pl : `PPlane` x : `float` y : `float` z : `float` Returns: `Box`	Creates a 3D box from PPlane and x, y and Z size. pl : `PPlane` x : `float` y : `float` z : `float` Returns: `Box`
`Box.createFromPlaneAndPoints pl pts` Full Usage: `Box.createFromPlaneAndPoints pl pts` Parameters: pl : `PPlane` pts : `IList<Pnt>` Returns: `Box`	Finds the oriented bounding box in 3D of a set of points. The orientation of the X-axis is defined by the dirX vector. The orientation of the Y-axis is defined by the dirY vector. pl : `PPlane` pts : `IList<Pnt>` Returns: `Box`
`Box.createFromRect2D (r, zLow, zHigh)` Full Usage: `Box.createFromRect2D (r, zLow, zHigh)` Parameters: r : `Rect2D` zLow : `float` zHigh : `float` Returns: `Box`	Creates a 3D box from a 2D rectangle and Z lower and upper position. r : `Rect2D` zLow : `float` zHigh : `float` Returns: `Box`
`Box.createFromRect3D (r, zLow, zHigh)` Full Usage: `Box.createFromRect3D (r, zLow, zHigh)` Parameters: r : `Rect3D` zLow : `float` zHigh : `float` Returns: `Box`	Creates a 3D box from a 3D rectangle and Z lower and upper position. r : `Rect3D` zLow : `float` zHigh : `float` Returns: `Box`
`Box.equals tol a b` Full Usage: `Box.equals tol a b` Parameters: tol : `float` a : `Box` b : `Box` Returns: `bool`	Checks if two 3D-boxes are equal within tolerance. Does not recognize congruent boxes with different rotation as equal. Use a tolerance of 0.0 to check for an exact match. tol : `float` a : `Box` b : `Box` Returns: `bool`
`Box.expand dist b` Full Usage: `Box.expand dist b` Parameters: dist : `float` b : `Box` Returns: `Box`	Returns Box expanded by distance on all six sides. Does check for underflow if distance is negative and raises EuclidException. dist : `float` b : `Box` Returns: `Box`
`Box.expandXYZ distX distY distZ b` Full Usage: `Box.expandXYZ distX distY distZ b` Parameters: distX : `float` distY : `float` distZ : `float` b : `Box` Returns: `Box`	Returns Box expanded by respective distances on all six sides. Does check for overflow if distance is negative and fails. distX, distY and distZ are for X, Y and Z-axis respectively. distX : `float` distY : `float` distZ : `float` b : `Box` Returns: `Box`
`Box.move v b` Full Usage: `Box.move v b` Parameters: v : `Vec` b : `Box` Returns: `Box`	Creates a 3D box moved by a vector. v : `Vec` b : `Box` Returns: `Box`
`Box.notEquals tol a b` Full Usage: `Box.notEquals tol a b` Parameters: tol : `float` a : `Box` b : `Box` Returns: `bool`	Check if two 3D-boxes are not equal within a given tolerance. Use a tolerance of 0.0 to check if the two 3D-boxes are not exactly equal. tol : `float` a : `Box` b : `Box` Returns: `bool`
`Box.transform m b` Full Usage: `Box.transform m b` Parameters: m : `RigidMatrix` b : `Box` Returns: `Box`	Transform the Box by the given RigidMatrix. The returned Box is guaranteed to have still orthogonal vectors. m : `RigidMatrix` b : `Box` Returns: `Box`
`Box.translateX distX b` Full Usage: `Box.translateX distX b` Parameters: distX : `float` b : `Box` Returns: `Box`	Creates a 3D box translated along the local X-axis of the Box. distX : `float` b : `Box` Returns: `Box`
`Box.translateY distY b` Full Usage: `Box.translateY distY b` Parameters: distY : `float` b : `Box` Returns: `Box`	Creates a 3D box translated along the local Y-axis of the Box. distY : `float` b : `Box` Returns: `Box`
`Box.translateZ distZ b` Full Usage: `Box.translateZ distZ b` Parameters: distZ : `float` b : `Box` Returns: `Box`	Creates a 3D box translated along the local Z-axis of the Box. distZ : `float` b : `Box` Returns: `Box`