Euclid
Rect3D Type
A struct containing a 3D Origin point and two 3D Edge vectors, representing an immutable planar 3D-rectangle with any rotation in 3D space. Similar to PPlane, however the two vectors are not unitized. This implementation guarantees the 3D-rectangle to be always valid. That means the X and Y axes are always perpendicular to each other. However the length of one of these axes might still be zero.
local
Y-axis
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+------------+-----> X-axis
0-Origin 1
Record fields
| Record Field |
Description
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Full Usage:
OriginX
Field type: float
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The X coordinate of the Origin Corner of the 3D-rectangle.
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Full Usage:
OriginY
Field type: float
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The Y coordinate of the Origin Corner of the 3D-rectangle.
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Full Usage:
OriginZ
Field type: float
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The Z coordinate of the Origin Corner of the 3D-rectangle.
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Full Usage:
XaxisX
Field type: float
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The X component of the edge vector representing the X-axis of the 3D-rectangle.
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Full Usage:
XaxisY
Field type: float
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The Y component of the edge vector representing the X-axis of the 3D-rectangle.
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Full Usage:
XaxisZ
Field type: float
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The Z component of the edge vector representing the X-axis of the 3D-rectangle.
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Full Usage:
YaxisX
Field type: float
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The X component of the edge vector representing the Y-axis of the 3D-rectangle.
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Full Usage:
YaxisY
Field type: float
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The Y component of the edge vector representing the Y-axis of the 3D-rectangle.
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Full Usage:
YaxisZ
Field type: float
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The Z component of the edge vector representing the Y-axis of the 3D-rectangle.
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Instance members
| Instance member |
Description
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Full Usage:
this.Area
Returns: float
Modifiers: inline |
Calculates the area of the 3D-rectangle.
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Full Usage:
this.AsFSharpCode
Returns: string
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Format Rect3D into an F# code string that can be used to recreate the rectangle.
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Full Usage:
this.AsString
Returns: string
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Format the 3D-rectangle into string with nice floating point number formatting of X and Y size only. But without type name as in v.ToString()
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Returns the center of the 3D-rectangle.
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Returns the X and Y parameters of the closest point on the 3D-rectangle to a given point. If the parameters are outside the range of 0.0 to 1.0, the closest point is outside the rectangle.
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Full Usage:
this.CountZeroSides
Returns: int
Modifiers: inline |
Counts the amount of sides that are smaller than the zeroLength tolerance. This is 0, 1, 2 .
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Returns the diagonal vector of the 3D-rectangle. From Origin to FarCorner.
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Returns the diagonal 3D line from point 0 to 2 of the 3D-rectangle.
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Returns a 3D line from point 0 to 1 of the 3D-rectangle.
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Returns a 3D line from point 1 to 2 of the 3D-rectangle.
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Returns a 3D line from point 2 to 3 of the 3D-rectangle.
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Returns a 3D line from point 3 to 0 of the 3D-rectangle.
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Returns the local X side as the 3D line from point 0 to 1 of the 3D-rectangle.
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Returns the local Y side as 3D line from point 0 to 3 of the 3D-rectangle. This is the reverse of Edge30.
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Returns the 4 Edges of the 3D-rectangle in counter-clockwise order, starting at Origin. Returns an array of 4 Lines: from point 0 to 1, 1 to 2, 2 to 3, 3 to 0.
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Full Usage:
this.EvaluateAt
Parameters:
float
yParameter : float
Returns: Pnt
Modifiers: inline |
Evaluate an X and Y parameter of the 3D rectangle. 0.0, 0.0 returns the Origin. 1.0, 1.0 returns the FarCorner.
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Full Usage:
this.EvaluateDist
Parameters:
float
yDistance : float
Returns: Pnt
Modifiers: inline |
Evaluate a point at X and Y distance on the respective axes of the 3D-rectangle.
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Returns the corner diagonally opposite of corner from Origin (point 2).
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Returns the rectangle flipped. Or rotated 180 around its diagonal from point 1 to 3. The normal of the rectangle gets flipped. Origin will be at point 2, X-axis points down to point 1, Y-axis points left to point 3.
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Returns one of the 4 Edges as 3D Line: Edge 0: from point 0 to 1 Edge 1: from point 1 to 2 Edge 2: from point 2 to 3 Edge 3: from point 3 to 0
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Full Usage:
this.HasArea
Returns: bool
Modifiers: inline |
Tests if neither the X nor Y-axis is smaller than the zeroLength tolerance. Same as .IsValid
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Full Usage:
this.IsLine
Returns: bool
Modifiers: inline |
Tests if one of the X and Y axes is smaller than the zeroLength tolerance.
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Full Usage:
this.IsPoint
Returns: bool
Modifiers: inline |
Tests if all sides are smaller than the zeroLength tolerance. Same as b.IsZero.
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this.IsValid
Returns: bool
Modifiers: inline |
Tests if neither the X nor Y-axis is smaller than the zeroLength tolerance. Same as .HasArea
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Full Usage:
this.IsZero
Returns: bool
Modifiers: inline |
Tests if all sides are smaller than the zeroLength tolerance. Same as b.IsPoint.
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Full Usage:
this.LongestEdge
Returns: float
Modifiers: inline |
Returns the longest edge of the Rect3D.
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Full Usage:
this.LongestEdgeSq
Returns: float
Modifiers: inline |
Returns the square length of longest edge of the Rect3D.
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Returns the Normal Resulting from the Cross Product of r.Xaxis with r.Yaxis.
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Returns the unitized Normal. Resulting from the Cross Product of r.Xaxis with r.Yaxis.
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Creates a 3D Point from r.OriginX, r.OriginY and r.OriginZ
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Gets the Plane that this 3D-rectangle is based on.
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Returns the 4 corners of the 3D-rectangle in counter-clockwise order, starting at Origin. Returns an array of 4 Points: point 0 then 1, 2 and 3.
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Returns the 4 corners of the 3D rectangle as a closed loop in counter-clockwise order, starting at Origin. First and last point are the same. Returns an array of 5 Points: point 0 then 1, 2, 3 and again 0.
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Full Usage:
this.PointsXYZ
Returns: ResizeArray<float>
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Returns the 4 corners of the 3D rectangle as an open loop of 12 floats, starting at Origin. Returns a ResizeArray of 12 floats: x, y, and z of point 0, point 1, point 2 and point 3.
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Full Usage:
this.PointsXYZLooped
Returns: ResizeArray<float>
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Returns the 5 corners of the 3D rectangle as closed loop of 15 floats, starting at Origin. Returns a ResizeArray of 15 floats: x, y, and z of point 0, point 1, point 2, point 3 and point 0 again.
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Returns point 0 of the 3D-rectangle. Same as member rect.Origin.
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Returns point 1 of the 3D-rectangle.
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Returns point 2 of the 3D-rectangle. Same as rect.FarCorner.
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Returns point 3 of the 3D-rectangle.
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Multiplies (or applies) a Quaternion to a 3D rectangle. The rectangle is rotated around the World Origin.
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Returns the rectangle rotated 180 degrees around its center. Returns the same rectangle with a new orientation rotated by 180 degrees around its center. This only changes the internal representation of the rectangle, the appearance is not changed. Origin will be at point 2, X-axis to point 3, Y-axis to point 1.
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Returns the same rectangle with a new orientation rotated by 90 degrees counter-clockwise around its center. This only changes the internal representation of the rectangle, the appearance is not changed. Origin will be at point 1, X-axis to point 2, Y-axis to point 0.
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Returns the same rectangle with a new orientation rotated by 90 degrees clockwise around its center. This only changes the internal representation of the rectangle, the appearance is not changed. Origin will be at point 3, X-axis to point 0, Y-axis to point 2.
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Full Usage:
this.RotateWithCenter
Parameters:
Pnt
q : Quaternion
Returns: Rect3D
Modifiers: inline |
Multiplies (or applies) a Quaternion to a 3D rectangle around a given center point.
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Scales the 3D rectangle by a given factor. Scale center is World Origin 0,0
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Full Usage:
this.ShortestEdge
Returns: float
Modifiers: inline |
Returns the shortest edge of the Rect3D.
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Full Usage:
this.ShortestEdgeSq
Returns: float
Modifiers: inline |
Returns the square length of shortest edge of the Rect3D.
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Full Usage:
this.SizeX
Returns: float
Modifiers: inline |
The size in X direction
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Full Usage:
this.SizeXSq
Returns: float
Modifiers: inline |
The squared size in X direction
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Full Usage:
this.SizeY
Returns: float
Modifiers: inline |
The size in Y direction
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Full Usage:
this.SizeYSq
Returns: float
Modifiers: inline |
The squared size in Y direction
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Multiplies (or applies) a RigidMatrix to a 3D rectangle. The returned 3D rectangle is guaranteed to have still orthogonal vectors.
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Returns the corner at end of X-axis (point 1).
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Creates a 3D Vector from r.XaxisX, r.XaxisY and r.XaxisZ
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Creates a unitized version of the local X-axis.
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Returns the corner at end of Y-axis (point 3).
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Creates a 3D Vector from r.YaxisX, r.YaxisY and r.YaxisZ
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Creates a unitized version of the local Y-axis.
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Static members
| Static member |
Description
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Format Rect3D into an F# code string that can be used to recreate the rectangle.
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Format the 3D-rectangle into string with nice floating point number formatting of X and Y size only.
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Creates a 3D-rectangle from three points. Fails if points are too close to each other or all collinear. The Origin, a point in X-axis direction and length, and a point for the length in Y-axis direction. Origin and x-point define the X-axis orientation of the Rectangle. The y-point only defines the length and side of the Y-axis.
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Full Usage:
Rect3D.createFromBounds2D (minX, minY, maxX, maxY)
Parameters:
float
minY : float
maxX : float
maxY : float
Returns: Rect3D
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Creates a 3D-rectangle from the given bounds in 2D. The rectangle will be in the XY-plane with Z=0.
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Full Usage:
Rect3D.createUnchecked (originX, originY, originZ, xAxisX, xAxisY, xAxisZ, yAxisX, yAxisY, yAxisZ)
Parameters:
float
originY : float
originZ : float
xAxisX : float
xAxisY : float
xAxisZ : float
yAxisX : float
yAxisY : float
yAxisZ : float
Returns: Rect3D
Modifiers: inline |
Create a 3D-rectangle from origin coordinates and X- and Y-axis vector components. Does not check for perpendicularity.
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Returns the 3D-rectangle expanded by a relative factor on all four sides. Values between 0.0 and 1.0 shrink the rectangle. Values larger than 1.0 expand the rectangle. Does check for underflow if factor is negative and raises EuclidException.
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Creates a new 3D rectangle( = oriented bounding rectangle ) to contain the projections of all given points. But not the corners of the reference rectangle. Keeps the same plane and the same X- and Y-axis orientation as the input rectangle. For a 3D oriented bounding box use the Box.createFromPlaneAndPoints function.
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Returns the rectangle flipped. Or rotated 180 around its diagonal from point 1 to 3. Origin will be at point 2, X-axis points down to point 1, Y-axis points left to point 3.
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Divides a 3D rectangle into a grid of points. It will create as few as points as possible respecting the maximum segment length. The input maxSegmentLength is multiplied by factor 1.00001 to avoid numerical errors. That means in an edge case there are fewer segments returned, not more. The returned array is divided along the X-axis. The sub-array is divided along the Y-axis.
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Divides a 3D rectangle into a grid of points. It will create as many points as possible respecting the minimum side length for x and y. The input minSegmentLength is multiplied by factor 0.9999 of to avoid numerical errors. That means in an edge case there are more segments returned, not fewer. The returned array is divided along the X-axis. The sub-array is divided along the Y-axis.
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Tests if neither the X nor Y-axis is smaller than the zeroLength tolerance. Same as Rect3D.isValid
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Returns intersection point of a Line3D with Rect3D. Returns ValueNone if the intersection point is outside their bounds. Use Rect3D.intersectRay to get the parameters of the intersection point. Returns ValueNone if they are parallel or coincident, or if the line has zero length. If the intersection parameters on the line and the rectangle are within 1e-6 of the bounds 0.0 or 1.0, it will still be considered as inside the rectangle and line.
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Returns the line parameter. The parameter is the intersection point of the ray with the infinitely extended Rect3D. The intersection point lies on the line segment itself only if the parameter is within the range 0.0 to 1.0. Returns ValueNone if they are parallel or coincident.
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Tests if all sides are smaller than the zeroLength tolerance. Same as Rect3D.isZero.
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Tests if neither the X nor Y-axis is smaller than the zeroLength tolerance. Same as Rect3D.hasArea
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Tests if all sides are smaller than the zeroLength tolerance. Same as Rect3D.isPoint.
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Full Usage:
Rect3D.iterPointsCCW action r
Parameters:
float -> float -> float -> unit
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The action to call 4 times. Once for each corner, with x, y and z as parameters.
r : Rect3D
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The rectangle to iterate the corners of.
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Iterates the 4 corners of the 3D rectangle in counter-clockwise order, starting at Origin.
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Full Usage:
Rect3D.iterPointsCW action r
Parameters:
float -> float -> float -> unit
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The action to call 4 times. Once for each corner, with x, y and z as parameters.
r : Rect3D
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The rectangle to iterate the corners of.
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Iterates the 4 corners of the 3D rectangle in Clockwise order, starting at Origin.
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Full Usage:
Rect3D.iterPointsLoopedCCW action r
Parameters:
float -> float -> float -> unit
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The action to call 5 times, with x, y and z as parameters.
r : Rect3D
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The rectangle to iterate the corners of.
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Iterates the 4 corners of the 3D rectangle as closed loop in counter-clockwise order, starting and ending at Origin.
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Full Usage:
Rect3D.iterPointsLoopedCW action r
Parameters:
float -> float -> float -> unit
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The action to call 5 times, with x, y and z as parameters.
r : Rect3D
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The rectangle to iterate the corners of.
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Iterates the 4 corners of the 3D rectangle as closed loop in Clockwise order, starting and ending at Origin.
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Full Usage:
Rect3D.offsetCorner (rect, corner, xOffset, yOffset, xWidth, yHeight)
Parameters:
Rect3D
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The 3D-rectangle
corner : int
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The Index of the corner to Offset
xOffset : float
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The local offset distances in x direction. (Applies to the y side.) Positive values offset to the inside of the rectangle, negative values will offset outwards.
yOffset : float
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The local offset distances in y direction. (Applies to the x side.) Positive values offset to the inside of the rectangle, negative values will offset outwards.
xWidth : float
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The width (or size in x direction) that will be added to the current offset.
yHeight : float
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The height (or size in y direction) that will be added to the current offset.
Returns: Rect3D
A new 3D-rectangle. It will always have the same X- and Y-axis orientation as the input rectangle. Independent of negative or positive offsets
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Offsets a local Rect3D at one of the four corners.
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Full Usage:
Rect3D.offsetEdge (rect, edgeIdx, offEdge, width, offStart, offEnd)
Parameters:
Rect3D
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The 3D-rectangle
edgeIdx : int
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The Index of the edge to offset
offEdge : float
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The local offset distances parallel to the edge.
width : float
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The width of the new rectangle. This is like the second offset to be applied to the first offset of offEdge
offStart : float
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The local offset distances perpendicular to the edge at the start.
offEnd : float
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The local offset distances perpendicular to the edge at the end.
Returns: Rect3D
A new 3D-rectangle. It will always have the same X- and Y-axis orientation as the input rectangle. Independent of negative or positive offsets
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Offsets a local Rect3D at one of the four edges.
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Offset a Rect3D like a Polyline inwards by four distances. The distance array is for Edge01, Edge12, Edge23, and Edge30 respectively. Fails if the distance is larger than half the size of the rectangle.
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Returns the 4 corners of the 3D rectangle as open loop, starting at Origin. Returns a ResizeArray of 12 floats: x, y, and z of point 0, point 1, point 2 and point 3.
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Full Usage:
Rect3D.pointsXYZLooped r
Parameters:
Rect3D
Returns: ResizeArray<float>
Modifiers: inline |
Returns the 5 corners of the 3D rectangle as a closed loop, starting at Origin. Returns a ResizeArray of 15 floats: x, y, and z of point 0, point 1, point 2, point 3 and point 0 again.
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Full Usage:
Rect3D.rotate q r
Parameters:
Quaternion
r : Rect3D
Returns: Rect3D
Modifiers: inline |
Multiplies (or applies) a Quaternion to a 3D rectangle. The rectangle is rotated around the World Origin.
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Full Usage:
Rect3D.rotateWithCenter cen q r
Parameters:
Pnt
q : Quaternion
r : Rect3D
Returns: Rect3D
Modifiers: inline |
Multiplies (or applies) a Quaternion to a 3D rectangle around a given center point.
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Divides a 3D-rectangle into a grid of sub-rectangles. The sub-rectangles are returned as an array of arrays. The gap between the sub-rectangles is given in x and y direction. It does not apply to the outer edges of the 3D-rectangle. The returned array has xCount elements, each element is an array of yCount sub-rectangles.
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Divides a 3D rectangle into a grid of sub-rectangles. The gap between the sub-rectangles is given in x and y direction. It does not apply to the outer edges of the 3D-rectangle. It will create as few segments as possible respecting the maximum segment length. The input maxSegmentLength is multiplied by factor 1.00001 to avoid numerical errors. That means in an edge case there are fewer segments returned, not more. The returned array is divided along the X-axis. The sub-array is divided along the Y-axis.
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Divides a 3D rectangle into a grid of sub-rectangles. The gap between the sub-rectangles is given in x and y direction. It does not apply to the outer edges of the 3D-rectangle. It will create as many sub-rectangles as possible, respecting the minimum side length for x and y. The input minSegmentLength is multiplied by factor 0.9999 to avoid numerical errors. That means in an edge case there are more segments returned, not fewer. The returned array is divided along the X-axis. The sub-array is divided along the Y-axis.
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Full Usage:
Rect3D.transformRigid m r
Parameters:
RigidMatrix
r : Rect3D
Returns: Rect3D
Modifiers: inline |
Transforms the 3D-rectangle by the given RigidMatrix. The returned 3D-rectangle is guaranteed to have orthogonal vectors.
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Tries to create a 3D-rectangle from three points. Returns None if points are too close to each other or all collinear. The Origin, a point in X-axis direction and length, and a point for the length in Y-axis direction. Origin and x-point define the X-axis orientation of the Rectangle. The y-point only defines the length and side of the Y-axis.
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