Namespace List

The namespaces specified in this document are:

Namespace	Assembly
Axiom.MathLib?	MathLib?
Axiom.MathLib.Collections?	MathLib?

Namespace : MathLib^?



MathLib^? Type List

Enumerations

Type	Summary
Intersection?	Type of intersection detected between 2 object.
PlaneSide?	The "positive side" of the plane is the half space to which the plane normal points. The "negative side" is the other half space. The flag "no side" indicates the plane itself.

Structs

Type	Summary
IntersectResult?	Simple struct to allow returning a complex intersection result.
Matrix3?	A 3x3 matrix which can represent rotations around axes.
Matrix4?	Class encapsulating a standard 4x4 homogenous matrix.
Plane?	Defines a plane in 3D space.
Quaternion?	Summary description for Quaternion.
Vector2?	2 dimensional vector.
Vector3?	Standard 3-dimensional vector.
Vector4?	4D homogeneous vector.

Classes

Type	Summary
AxisAlignedBox?	A 3D box aligned with the x/y/z axes.
MathUtil?	This is a class which exposes static methods for various common math functions. Currently, the methods simply wrap the methods of the System.Math class (with the exception of a few added extras). This is in case the implementation needs to be swapped out with a faster C++ implementation, if deemed that the System.Math methods are not up to far speed wise.
PlaneBoundedVolume?	Represents a convex volume bounded by planes.
PositionalSpline?	A Catmull-Rom spline that can be used for interpolating translation movements.
Ray?	Representation of a ray in space, ie a line with an origin and direction.
RotationalSpline?	A class used to interpolate orientations (rotations) along a spline using derivatives of quaternions.
Sphere?	A standard sphere, used mostly for bounds checking.



MathLib^? Enumerations

Intersection Enumeration

Summary

public enumeration Intersection

Type of intersection detected between 2 object.

Remarks

Type of intersection detected between 2 object.

Enumeration Members

Field	Summary
Contained	An object is fully contained within another object.
Contains	An object fully contains another object.
None	The objects are not intersecting.
Partial	The objects are partially intersecting each other.

PlaneSide Enumeration

Summary

public enumeration PlaneSide?

The "positive side" of the plane is the half space to which the plane normal points. The "negative side" is the other half space. The flag "no side" indicates the plane itself.

Remarks

The "positive side" of the plane is the half space to which the plane normal points. The "negative side" is the other half space. The flag "no side" indicates the plane itself.

Enumeration Members

Field	Summary
Negative
None
Positive



MathLib^? Structs

Vector2 Structure

Summary

public structure Vector2

2 dimensional vector.

Remarks

2 dimensional vector.

Constructor Members

Name	Access	Summary
Vector2()	public	Constructor.

Field Members

Name	Access	Summary
x : Single	public
y : Single	public

Method Members

Name	Access	Summary
Add() : Vector2	public	Used when a Vector2 is added to another Vector2.
Multiply() : Vector2	public	Used when a Vector2 is multiplied by a scalar value.
Multiply() : Vector2	public	Used when a scalar value is multiplied by a Vector2.
Negate() : Vector2	public	Used to negate the elements of a vector.
Subtract() : Vector2	public	Used to subtract a Vector2 from another Vector2.

Quaternion Structure

Summary

public structure Quaternion

Summary description for Quaternion.

Remarks

Summary description for Quaternion.

Constructor Members

Name	Access	Summary
Quaternion()	public	Creates a new Quaternion.

Field Members

Name	Access	Summary
w : Single	public
x : Single	public
y : Single	public
z : Single	public

Property Members

Name	Access	Summary
Identity : Quaternion	public	An Identity Quaternion.
Norm : Single	public	Squared 'length' of this quaternion.
XAxis : Vector3	public	Local X-axis portion of this rotation.
YAxis : Vector3	public	Local Y-axis portion of this rotation.
ZAxis : Vector3	public	Local Z-axis portion of this rotation.
Zero : Quaternion	public	A Quaternion with all elements set to 0.0f;

Method Members

Name	Access	Summary
Add() : Quaternion	public	Used when a Quaternion is added to another Quaternion.
Dot() : Single	public	Performs a Dot Product operation on 2 Quaternions.
Equals() : Boolean	public
Exp() : Quaternion	public	Calculates the Exponent of a Quaternion.
FromAngleAxis?() : Quaternion	public	Creates a Quaternion from a supplied angle and axis.
FromAxes?() : Void	public
FromRotationMatrix?() : Void	public
GetHashCode?() : Int32	public
Inverse() : Quaternion	public	Computes the inverse of a Quaternion.
Log() : Quaternion	public	Calculates the logarithm of a Quaternion.
Multiply() : Quaternion	public	Used to multiply 2 Quaternions together.
Multiply() : Vector3	public
Multiply() : Quaternion	public	Used when a Quaternion is multiplied by a float value.
Multiply() : Quaternion	public	Used when a float value is multiplied by a Quaternion.
Normalize() : Void	public	Normalizes elements of this quaterion to the range [0,1].
Slerp() : Quaternion	public
Slerp() : Quaternion	public
Squad() : Quaternion	public
Squad() : Quaternion	public	Performs spherical quadratic interpolation.
ToAngleAxis?() : Void	public
ToAxes?() : Void	public
ToRotationMatrix?() : Matrix3	public	Gets a 3x3 rotation matrix from this Quaternion.
ToString?() : String	public	Overrides the ToString?() method to provide a text representation of a Quaternion.

Plane Structure

Summary

public structure Plane

Defines a plane in 3D space.

Remarks

A plane is defined in 3D space by the equation Ax + By + Cz + D = 0 This equates to a vector (the normal of the plane, whose x, y and z components equate to the coefficients A, B and C respectively), and a constant (D) which is the distance along the normal you have to go to move the plane back to the origin.

Constructor Members

Name	Access	Summary
Plane()	public
Plane()	public
Plane()	public	Construct a plane from 3 coplanar points.
Plane()	public	Construct a plane through a normal, and a distance to move the plane along the normal.

Field Members

Name	Access	Summary
D : Single	public	Distance from the origin.
Normal : Vector3	public	Direction the plane is facing.

Method Members

Name	Access	Summary
Equals() : Boolean	public	Object method for testing equality.
GetDistance?() : Single	public	This is a pseudodistance. The sign of the return value is positive if the point is on the positive side of the plane, negative if the point is on the negative side, and zero if the point is on the plane. The absolute value of the return value is the true distance only when the plane normal is a unit length vector.
GetHashCode?() : Int32	public	Gets the hashcode for this Plane.
GetSide?() : PlaneSide?	public
Redefine() : Void	public	Construct a plane from 3 coplanar points.
ToString?() : String	public	Returns a string representation of this Plane.

IntersectResult Structure

Summary

public structure IntersectResult?

Simple struct to allow returning a complex intersection result.

Remarks

Simple struct to allow returning a complex intersection result.

Constructor Members

Name	Access	Summary
IntersectResult?()	public	Constructor.

Field Members

Name	Access	Summary
Distance : Single	public	If Hit was true, this will hold a query specific distance value. i.e. for a Ray-Box test, the distance will be the distance from the start point of the ray to the point of intersection.
Hit : Boolean	public	Did the intersection test result in a hit?

Method Members

Name	Access	Summary

Matrix4 Structure

Summary

public structure Matrix4

Class encapsulating a standard 4x4 homogenous matrix.

Remarks

The engine uses column vectors when applying matrix multiplications, This means a vector is represented as a single column, 4-row matrix. This has the effect that the tranformations implemented by the matrices happens right-to-left e.g. if vector V is to be transformed by M1 then M2 then M3, the calculation would be M3 * M2 * M1 * V. The order that matrices are concatenated is vital since matrix multiplication is not cummatative, i.e. you can get a different result if you concatenate in the wrong order.

The use of column vectors and right-to-left ordering is the standard in most mathematical texts, and is the same as used in OpenGL^?. It is, however, the opposite of Direct3D, which has inexplicably chosen to differ from the accepted standard and uses row vectors and left-to-right matrix multiplication.

The engine deals with the differences between D3D and OpenGL^? etc. internally when operating through different render systems. The engine users only need to conform to standard maths conventions, i.e. right-to-left matrix multiplication, (The engine transposes matrices it passes to D3D to compensate).

The generic form M * V which shows the layout of the matrix entries is shown below:

| m[0][0] m[0][1] m[0][2] m[0][3] | {x} | m[1][0] m[1][1] m[1][2] m[1][3] | {y} | m[2][0] m[2][1] m[2][2] m[2][3] | {z} | m[3][0] m[3][1] m[3][2] m[3][3] | {1}

Constructor Members

Name	Access	Summary
Matrix4()	public	Creates a new Matrix4 with all the specified parameters.

Field Members

Name	Access	Summary
m00 : Single	public
m01 : Single	public
m02 : Single	public
m03 : Single	public
m10 : Single	public
m11 : Single	public
m12 : Single	public
m13 : Single	public
m20 : Single	public
m21 : Single	public
m22 : Single	public
m23 : Single	public
m30 : Single	public
m31 : Single	public
m32 : Single	public
m33 : Single	public

Property Members

Name	Access	Summary
ClipSpace2DToImageSpace? : Matrix4	public
Determinant : Single	public	Gets the determinant of this matrix.
Identity : Matrix4	public	Returns a matrix with the following form:	1,0,0,0		0,1,0,0		0,0,1,0		0,0,0,1
Item : Single	public	Allows the Matrix to be accessed linearly (m[0] -> m[15]).
Item : Single	public	Allows the Matrix to be accessed like a 2d array (i.e. matrix[2,3])
Scale : Vector3	public	Gets/Sets the Translation portion of the matrix.	Sx 0 0 0		0 Sy 0 0		0 0 Sz 0		0 0 0 0
Translation : Vector3	public	Gets/Sets the Translation portion of the matrix.	0 0 0 Tx		0 0 0 Ty		0 0 0 Tz		0 0 0 1
Zero : Matrix4	public	Returns a matrix with all elements set to 0.

Method Members

Name	Access	Summary
Add() : Matrix4	public	Used to add two matrices together.
Equals() : Boolean	public	Compares this Matrix to another object. This should be done because the equality operators (=, ) have been overriden by this class.
FromMatrix3?() : Matrix4	public	Used to allow assignment from a Matrix3 to a Matrix4 object.
GetHashCode?() : Int32	public	Provides a unique hash code based on the member variables of this class. This should be done because the equality operators (=, ) have been overriden by this class. The standard implementation is a simple XOR operation between all local member variables.
GetMatrix3?() : Matrix3	public	Returns a 3x3 portion of this 4x4 matrix.
Inverse() : Matrix4	public	Returns an inverted 4d matrix.
MakeFloatArray?() : Void	public
Multiply() : Matrix4	public	Used to multiply (concatenate) two 4x4 Matrices.
Multiply() : Plane	public	Transforms a plane using the specified transform.
Multiply() : Vector3	public	Transforms the given 3-D vector by the matrix, projecting the result back into w = 1. This means that the initial w is considered to be 1.0, and then all the tree elements of the resulting 3-D vector are divided by the resulting w.
Subtract() : Matrix4	public	Used to subtract two matrices.
ToString?() : String	public	Overrides the ToString?() method to provide a text representation of a Matrix4.
Transpose() : Matrix4	public	Swap the rows of the matrix with the columns.

Matrix3 Structure

Summary

public structure Matrix3

A 3x3 matrix which can represent rotations around axes.

Remarks

A 3x3 matrix which can represent rotations around axes.

Constructor Members

Name	Access	Summary
Matrix3()	public	Create a new Matrix from 3 Vertex3 objects.
Matrix3()	public	Creates a new Matrix3 with all the specified parameters.

Field Members

Name	Access	Summary
m00 : Single	public
m01 : Single	public
m02 : Single	public
m10 : Single	public
m11 : Single	public
m12 : Single	public
m20 : Single	public
m21 : Single	public
m22 : Single	public

Property Members

Name	Access	Summary
Determinant : Single	public
Identity : Matrix3	public	Identity Matrix
Item : Single	public	Allows the Matrix to be accessed linearly (m[0] -> m[8]).
Item : Single	public	Indexer for accessing the matrix like a 2d array (i.e. matrix[2,3]).
Zero : Matrix3	public	Zero matrix.

Method Members

Name	Access	Summary
Add() : Matrix3	public	Used to add two matrices together.
Equals() : Boolean	public	Compares this Matrix to another object. This should be done because the equality operators (=, ) have been overriden by this class.
FromAxes?() : Void	public	Creates a Matrix3 from 3 axes.
FromEulerAnglesXYZ?() : Void	public	Constructs this Matrix from 3 euler angles, in degrees.
GetColumn?() : Vector3	public	Gets a matrix column by index.
GetHashCode?() : Int32	public	Provides a unique hash code based on the member variables of this class. This should be done because the equality operators (=, ) have been overriden by this class. The standard implementation is a simple XOR operation between all local member variables.
Multiply() : Matrix3	public	Multiply (concatenate) two Matrix3 instances together.
Multiply() : Vector3	public	matrix * vector [3x3 * 3x1 = 3x1]
Multiply() : Matrix3	public	Multiplies all the items in the Matrix3 by a scalar value.
Multiply() : Vector3	public	vector * matrix [1x3 * 3x3 = 1x3]
Multiply() : Matrix3	public	Multiplies all the items in the Matrix3 by a scalar value.
Negate() : Matrix3	public	Negates all the items in the Matrix.
SetColumn?() : Void	public	Sets one of the columns of the Matrix with a Vector3.
Subtract() : Matrix3	public	Used to subtract two matrices.
ToString?() : String	public	Overrides the ToString?() method to provide a text representation of a Matrix4.
Transpose() : Matrix3	public	Swap the rows of the matrix with the columns.

Vector4 Structure

Summary

public structure Vector4

4D homogeneous vector.

Remarks

4D homogeneous vector.

Constructor Members

Name	Access	Summary
Vector4()	public	Creates a new 4 dimensional Vector.

Field Members

Name	Access	Summary
w : Single	public
x : Single	public
y : Single	public
z : Single	public

Property Members

Name	Access	Summary
Item : Single	public	Used to access a Vector by index 0 = this.x, 1 = this.y, 2 = this.z, 3 = this.w.

Method Members

Name	Access	Summary
Dot() : Single	public	Calculates the dot (scalar) product of this vector with another.
Equals() : Boolean	public	Compares this Vector to another object. This should be done because the equality operators (=, ) have been overriden by this class.
GetHashCode?() : Int32	public	Provides a unique hash code based on the member variables of this class. This should be done because the equality operators (=, ) have been overriden by this class. The standard implementation is a simple XOR operation between all local member variables.
Multiply() : Vector4	public
ToString?() : String	public	Overrides the ToString?() method to provide a text representation of a Vector4.

Vector3 Structure

Summary

public structure Vector3

Standard 3-dimensional vector.

Remarks

A direction in 3D space represented as distances along the 3 orthoganal axes (x, y, z). Note that positions, directions and scaling factors can be represented by a vector, depending on how you interpret the values.

Constructor Members

Name	Access	Summary
Vector3()	public	Creates a new 3 dimensional Vector.

Field Members

Name	Access	Summary
x : Single	public	X component.
y : Single	public	Y component.
z : Single	public	Z component.

Property Members

Name	Access	Summary
Item : Single	public	Used to access a Vector by index 0 = x, 1 = y, 2 = z.
Length : Single	public	Gets the length (magnitude) of this Vector3. The Sqrt operation is expensive, so only use this if you need the exact length of the Vector. If vector lengths are only going to be compared, use LengthSquared? instead.
LengthSquared? : Single	public	Returns the length (magnitude) of the vector squared.
NegativeUnitX? : Vector3	public	Gets a Vector3 with the X set to -1, and the others set to 0.
NegativeUnitY? : Vector3	public	Gets a Vector3 with the Y set to -1, and the others set to 0.
NegativeUnitZ? : Vector3	public	Gets a Vector3 with the Z set to -1, and the others set to 0.
UnitScale? : Vector3	public	Gets a Vector3 with all components set to 1.
UnitX? : Vector3	public	Gets a Vector3 with the X set to 1, and the others set to 0.
UnitY? : Vector3	public	Gets a Vector3 with the Y set to 1, and the others set to 0.
UnitZ? : Vector3	public	Gets a Vector3 with the Z set to 1, and the others set to 0.
Zero : Vector3	public	Gets a Vector3 with all components set to 0.

Method Members

Name	Access	Summary
Add() : Vector3	public	Used when a Vector3 is added to another Vector3.
Ceil() : Void	public	Compares the supplied vector and updates it's x/y/z components of they are higher in value.
Cross() : Vector3	public	Performs a Cross Product operation on 2 vectors, which returns a vector that is perpendicular to the intersection of the 2 vectors. Useful for finding face normals.
Divide() : Vector3	public	Used to divide a vector by a scalar value.
Dot() : Single	public	Performs a Dot Product operation on 2 vectors, which returns a single number obtained by multiplying corresponding axis values and adding up these products.
Equals() : Boolean	public	Compares this Vector to another object. This should be done because the equality operators (=, ) have been overriden by this class.
Floor() : Void	public	Compares the supplied vector and updates it's x/y/z components of they are lower in value.
GetHashCode?() : Int32	public	Provides a unique hash code based on the member variables of this class. This should be done because the equality operators (=, ) have been overriden by this class. The standard implementation is a simple XOR operation between all local member variables.
GetRotationTo?() : Quaternion	public	Gets the shortest arc quaternion to rotate this vector to the destination vector.
MidPoint?() : Vector3	public	Finds the midpoint between the supplied Vector and this vector.
Multiply() : Vector3	public	Used when a Vector3 is multiplied by another vector.
Multiply() : Vector3	public	Used when a Vector3 is multiplied by a scalar value.
Multiply() : Vector3	public	Used when a scalar value is multiplied by a Vector3.
Negate() : Vector3	public	Used to negate the elements of a vector.
Normalize() : Single	public	Normalizes the vector.
Perpendicular() : Vector3	public	Finds a vector perpendicular to this one.
RandomDeviant?() : Vector3	public
Reflect() : Vector3	public	Calculates a reflection vector to the plane with the given normal.
Subtract() : Vector3	public	Used to subtract a Vector3 from another Vector3.
ToString?() : String	public	Overrides the ToString?() method to provide a text representation of a Vector3.



MathLib^? Classes

AxisAlignedBox Class

Summary

public class AxisAlignedBox? : System.ICloneable

A 3D box aligned with the x/y/z axes.

Remarks

This class represents a simple box which is aligned with the axes. Internally it only stores 2 points as the extremeties of the box, one which is the minima of all 3 axes, and the other which is the maxima of all 3 axes. This class is typically used for an axis-aligned bounding box (AABB) for collision and visibility determination.

Constructor Members

Name	Access	Summary
AxisAlignedBox?()	public	Initializes a new instance of the class.
AxisAlignedBox?()	public

Property Members

Name	Access	Summary
Center : Vector3	public	Gets the center point of this bounding box.
Corners : Vector3[]	public	Returns an array of 8 corner points, useful for collision vs. non-aligned objects.
IsNull? : Boolean	public	Gets/Sets the value of whether this box is null (i.e. not dimensions, etc).
Maximum : Vector3	public	Gets/Sets the maximum corner of the box.
Minimum : Vector3	public	Gets/Sets the minimum corner of the box.
Null : AxisAlignedBox?	public	Returns a null box

Method Members

Name	Access	Summary
Clone() : Object	public
Intersects() : Boolean	public	Returns whether or not this box intersects another.
Intersects() : Boolean	public
Intersects() : Boolean	public	Tests whether this box intersects a sphere.
Intersects() : Boolean	public	Tests whether the vector point is within this box.
Merge() : Void	public	Allows for merging two boxes together (combining).
Scale() : Void	public	Scales the size of the box by the supplied factor.
SetExtents?() : Void	public	Sets both Minimum and Maximum at once, so that UpdateCorners? only needs to be called once as well.
Transform() : Void	public

RotationalSpline Class

Summary

public class RotationalSpline?

A class used to interpolate orientations (rotations) along a spline using derivatives of quaternions.

Remarks

Like the PositionalSpline^? class, this class is about interpolating values smoothly over a spline. Whilst PositionalSpline^? deals with positions (the normal sense we think about splines), this class interpolates orientations. The theory is identical, except we're now in 4-dimensional space instead of 3.

In positional splines, we use the points and tangents on those points to generate control points for the spline. In this case, we use quaternions and derivatives of the quaternions (i.e. the rate and direction of change at each point). This is the same as PositionalSpline^? since a tangent is a derivative of a position. We effectively generate an extra quaternion in between each actual quaternion which when take with the original quaternion forms the 'tangent' of that quaternion.

Constructor Members

Name	Access	Summary
RotationalSpline?()	public	Creates a new Rotational Spline.

Property Members

Name	Access	Summary
AutoCalculate? : Boolean	public	Specifies whether or not to recalculate tangents as each control point is added.
PointCount? : Int32	public	Gets the number of control points in this spline.

Method Members

Name	Access	Summary
AddPoint?() : Void	public	Adds a control point to the end of the spline.
Clear() : Void	public	Removes all current control points from this spline.
Interpolate() : Quaternion	public
Interpolate() : Quaternion	public	Interpolates a single segment of the spline given a parametric value.
Interpolate() : Quaternion	public
Interpolate() : Quaternion	public	Returns an interpolated point based on a parametric value over the whole series.
RecalculateTangents?() : Void	public	Recalculates the tangents associated with this spline.

Sphere Class

Summary

public class Sphere

A standard sphere, used mostly for bounds checking.

Remarks

A sphere in math texts is normally represented by the function x^2 + y^2 + z^2 = r^2 (for sphere's centered on the origin). We store spheres simply as a center point and a radius.

Constructor Members

Name	Access	Summary
Sphere()	public	Creates a unit sphere centered at the origin.
Sphere()	public	Creates an arbitrary spehere.

Property Members

Name	Access	Summary
Center : Vector3	public	Gets/Sets the center of the sphere.
Radius : Single	public	Gets/Sets the radius of the sphere.

Method Members

Name	Access	Summary
Intersects() : Boolean	public	Returns whether or not this sphere interects a box.
Intersects() : Boolean	public	Returns whether or not this sphere interects a plane.
Intersects() : Boolean	public	Tests for intersection between this sphere and another sphere.
Intersects() : Boolean	public	Returns whether or not this sphere interects a Vector3.

PositionalSpline Class

Summary

public class PositionalSpline?

A Catmull-Rom spline that can be used for interpolating translation movements.

Remarks

A Catmull-Rom spline is a derivitive of the Hermite spline. The difference is that the Hermite spline allows you to specifiy 2 endpoints and 2 tangents, then the spline is generated. A Catmull-Rom spline allows you to just supply 1-n number of points and the tangents will be automatically calculated.

Derivation of the hermite polynomial can be found here: Hermite splines.

Constructor Members

Name	Access	Summary
PositionalSpline?()	public	Creates a new Positional Spline.

Property Members

Name	Access	Summary
AutoCalculate? : Boolean	public	Specifies whether or not to recalculate tangents as each control point is added.
PointCount? : Int32	public	Gets the number of control points in this spline.

Method Members

Name	Access	Summary
AddPoint?() : Void	public	Adds a new control point to the end of this spline.
Clear() : Void	public	Removes all current control points from this spline.
GetPoint?() : Vector3	public	Returns the point at the specified index.
Interpolate() : Vector3	public	Interpolates a single segment of the spline given a parametric value.
Interpolate() : Vector3	public	Returns an interpolated point based on a parametric value over the whole series.
RecalculateTangents?() : Void	public	Recalculates the tangents associated with this spline.

Ray Class

Summary

public class Ray

Representation of a ray in space, ie a line with an origin and direction.

Remarks

Representation of a ray in space, ie a line with an origin and direction.

Constructor Members

Name	Access	Summary
Ray()	public	Default constructor.
Ray()	public	Constructor.

Property Members

Name	Access	Summary
Direction : Vector3	public	Gets/Sets the direction this ray is pointing.
Origin : Vector3	public	Gets/Sets the origin of the ray.

Method Members

Name	Access	Summary
Intersects() : IntersectResult?	public	Tests whether this ray intersects the given box.
Intersects() : IntersectResult?	public	Tests whether this ray intersects the given plane.
Intersects() : IntersectResult?	public	Tests whether this ray intersects the given PlaneBoundedVolume?.
Intersects() : IntersectResult?	public	Tests whether this ray intersects the given sphere.

PlaneBoundedVolume Class

Summary

public class PlaneBoundedVolume?

Represents a convex volume bounded by planes.

Remarks

Represents a convex volume bounded by planes.

Constructor Members

Name	Access	Summary
PlaneBoundedVolume?()	public	Default constructor.
PlaneBoundedVolume?()	public	Constructor.

Field Members

Name	Access	Summary
outside : PlaneSide?	public	Side of the plane to be considered 'outside'.
planes : PlaneList?	public	Publicly accessible plane list, you can modify this direct.

Method Members

Name	Access	Summary
Intersects() : Boolean	public	Intersection test with an .
Intersects() : Boolean	public	Intersection test with .

MathUtil Class

Summary

public class MathUtil?

This is a class which exposes static methods for various common math functions. Currently, the methods simply wrap the methods of the System.Math class (with the exception of a few added extras). This is in case the implementation needs to be swapped out with a faster C++ implementation, if deemed that the System.Math methods are not up to far speed wise.

Remarks

Field Members

Name	Access	Summary
DEGREES_PER_RADIAN : Single	public
PI : Single	public
RADIANS_PER_DEGREE : Single	public
TWO_PI : Single	public

Method Members

Name	Access	Summary
Abs() : Single	public	Returns the absolute value of the supplied number.
ACos() : Single	public	Returns the arc cosine of the angle.
ASin() : Single	public	Returns the arc sine of the angle.
BuildReflectionMatrix?() : Matrix4	public	Builds a reflection matrix for the specified plane.
CalculateBasicFaceNormal?() : Vector3	public	Calculate a face normal, no w-information.
CalculateFaceNormal?() : Vector4	public	Calculate a face normal, including the w component which is the offset from the origin.
CalculateTangentSpaceVector?() : Vector3	public	Calculates the tangent space vector for a given set of positions / texture coords.
Cos() : Single	public	Returns the cosine of the angle.
DegreesToRadians?() : Single	public	Converts degrees to radians.
FloatEqual?() : Boolean	public
FloatEqual?() : Boolean	public	Compares float values for equality, taking into consideration that floating point values should never be directly compared using ==. 2 floats could be conceptually equal, but vary by a .000001 which would fail in a direct comparison. To circumvent that, a tolerance value is used to see if the difference between the 2 floats is less than the desired amount of accuracy.
Intersects() : Intersection	public	Tests an intersection between two boxes.
Intersects() : Boolean	public	Plane/Box intersection test.
Intersects() : IntersectResult?	public	Tests an intersection between a ray and a box.
Intersects() : IntersectResult?	public	Ray/Plane intersection test.
Intersects() : IntersectResult?	public	Ray/PlaneBoundedVolume intersection test.
Intersects() : IntersectResult?	public
Intersects() : IntersectResult?	public	Ray/Sphere intersection test.
Intersects() : Boolean	public	Sphere/Box intersection test.
Intersects() : Boolean	public	Sphere/Plane intersection test.
InvSqrt?() : Single	public	Inverse square root.
Max() : Single	public	Used to quickly determine the greater value between two values.
Min() : Single	public	Used to quickly determine the lesser value between two values.
PointInTri2D?() : Boolean	public	Checks wether a given point is inside a triangle, in a 2-dimensional (Cartesian) space.
RadiansToDegrees?() : Single	public	Converts radians to degrees.
RangeRandom?() : Single	public	Returns a random value between the specified min and max values.
Sin() : Single	public	Returns the sine of the angle.
Sqrt() : Single	public	Returns the square root of a number.
SymmetricRandom?() : Single	public
Tan() : Single	public	Returns the tangent of the angle.
UnitRandom?() : Single	public

Namespace : MathLib^?.Collections



MathLib^?.Collections Type List

Interfaces

Type	Summary
QuaternionCollection.IQuaternionCollectionEnumerator	Supports type-safe iteration over a .
Vector3List.IVector3ListEnumerator	Supports type-safe iteration over a .

Enumerations

Type	Summary
QuaternionCollection.Tag
Vector3List.Tag

Classes

Type	Summary
BaseCollection	Serves as a basis for strongly typed collections in the math lib.
Pair	A simple container class for returning a pair of objects from a method call (similar to std::pair, minus the templates).
PlaneBoundedVolumeList	Initializes a new instance of the class.
PlaneList	Initializes a new instance of the class.
QuaternionCollection	A strongly-typed collection of objects.
Vector3List	A strongly-typed collection of objects.



MathLib^?.Collections Interfaces

QuaternionCollection.IQuaternionCollectionEnumerator Interface

Summary

nestedPublic interface IQuaternionCollectionEnumerator?

Supports type-safe iteration over a .

Remarks

Supports type-safe iteration over a .

Property Members

Name	Access	Summary
Current : Quaternion	public	Gets the current element in the collection.

Method Members

Name	Access	Summary
MoveNext?() : Boolean	public	Advances the enumerator to the next element in the collection.
Reset() : Void	public	Sets the enumerator to its initial position, before the first element in the collection.

Vector3List.IVector3ListEnumerator Interface

Summary

nestedPublic interface Vector3List.IVector3ListEnumerator

Supports type-safe iteration over a .

Remarks

Supports type-safe iteration over a .

Property Members

Name	Access	Summary
Current : Vector3	public	Gets the current element in the collection.

Method Members

Name	Access	Summary
MoveNext?() : Boolean	public	Advances the enumerator to the next element in the collection.
Reset() : Void	public	Sets the enumerator to its initial position, before the first element in the collection.



MathLib^?.Collections Enumerations

QuaternionCollection.Tag Enumeration

Summary

nestedFamily enumeration QuaternionCollection?.Tag

Enumeration Members

Field	Summary
Default

Vector3List.Tag Enumeration

Summary

nestedFamily enumeration Vector3List.Tag

Enumeration Members

Field	Summary
Default



MathLib^?.Collections Classes

Pair Class

Summary

public class Pair

A simple container class for returning a pair of objects from a method call (similar to std::pair, minus the templates).

Remarks

Constructor Members

Name	Access	Summary
Pair()	public

Field Members

Name	Access	Summary
first : Object	public
second : Object	public

Method Members

Name	Access	Summary

QuaternionCollection Class

Summary

public class QuaternionCollection? : System.Collections.IList, System.Collections.ICollection, System.Collections.IEnumerable, System.ICloneable

A strongly-typed collection of objects.

This type has the following attributes: SerializableAttribute^?

Remarks

A strongly-typed collection of objects.

Constructor Members

Name	Access	Summary
QuaternionCollection?()	public	Initializes a new instance of the QuaternionCollection? class that is empty and has the default initial capacity.
QuaternionCollection?()	public	Initializes a new instance of the QuaternionCollection? class that contains elements copied from the specified QuaternionCollection?.
QuaternionCollection?()	protected
QuaternionCollection?()	public	Initializes a new instance of the QuaternionCollection? class that contains elements copied from the specified array.
QuaternionCollection?()	public	Initializes a new instance of the QuaternionCollection? class that has the specified initial capacity.

Property Members

Name	Access	Summary
Capacity : Int32	public	Gets or sets the number of elements the QuaternionCollection? can contain.
Count : Int32	public	Gets the number of elements actually contained in the QuaternionCollection?.
IsFixedSize? : Boolean	public	Gets a value indicating whether the collection has a fixed size.
IsReadOnly? : Boolean	public	gets a value indicating whether the IList is read-only.
IsSynchronized? : Boolean	public	Gets a value indicating whether access to the collection is synchronized (thread-safe).
Item : Quaternion	public	Gets or sets the at the specified index.
SyncRoot? : Object	public	Gets an object that can be used to synchronize access to the collection.

Method Members

Name	Access	Summary
Add() : Int32	public	Adds a to the end of the QuaternionCollection?.
AddRange?() : Int32	public	Adds the elements of another QuaternionCollection? to the current QuaternionCollection?.
AddRange?() : Int32	public	Adds the elements of a array to the current QuaternionCollection?.
Clear() : Void	public	Removes all elements from the QuaternionCollection?.
Clone() : Object	public	Creates a shallow copy of the .
Contains() : Boolean	public	Determines whether a given is in the QuaternionCollection?.
CopyTo?() : Void	public	Copies the entire QuaternionCollection? to a one-dimensional array.
CopyTo?() : Void	public	Copies the entire QuaternionCollection? to a one-dimensional array, starting at the specified index of the target array.
GetEnumerator?() : IQuaternionCollectionEnumerator?	public	Returns an enumerator that can iterate through the QuaternionCollection?.
IndexOf?() : Int32	public	Returns the zero-based index of the first occurrence of a in the QuaternionCollection?.
Insert() : Void	public	Inserts an element into the QuaternionCollection? at the specified index.
ReadOnly?() : QuaternionCollection?	public	Creates a read-only wrapper for a QuaternionCollection? instance.
Remove() : Void	public	Removes the first occurrence of a specific from the QuaternionCollection?.
RemoveAt?() : Void	public	Removes the element at the specified index of the QuaternionCollection?.
Synchronized() : QuaternionCollection?	public	Creates a synchronized (thread-safe) wrapper for a QuaternionCollection? instance.
TrimToSize?() : Void	public	Sets the capacity to the actual number of elements.

Vector3List Class

Summary

public class Vector3List : System.Collections.IList, System.Collections.ICollection, System.Collections.IEnumerable, System.ICloneable

A strongly-typed collection of objects.

This type has the following attributes: SerializableAttribute^?

Remarks

A strongly-typed collection of objects.

Constructor Members

Name	Access	Summary
Vector3List()	public	Initializes a new instance of the Vector3List class that is empty and has the default initial capacity.
Vector3List()	public	Initializes a new instance of the Vector3List class that contains elements copied from the specified Vector3List.
Vector3List()	protected
Vector3List()	public	Initializes a new instance of the Vector3List class that contains elements copied from the specified array.
Vector3List()	public	Initializes a new instance of the Vector3List class that has the specified initial capacity.

Property Members

Name	Access	Summary
Capacity : Int32	public	Gets or sets the number of elements the Vector3List can contain.
Count : Int32	public	Gets the number of elements actually contained in the Vector3List.
IsFixedSize? : Boolean	public	Gets a value indicating whether the collection has a fixed size.
IsReadOnly? : Boolean	public	gets a value indicating whether the IList is read-only.
IsSynchronized? : Boolean	public	Gets a value indicating whether access to the collection is synchronized (thread-safe).
Item : Vector3	public	Gets or sets the at the specified index.
SyncRoot? : Object	public	Gets an object that can be used to synchronize access to the collection.

Method Members

Name	Access	Summary
Add() : Int32	public	Adds a to the end of the Vector3List.
AddRange?() : Int32	public	Adds the elements of another Vector3List to the current Vector3List.
AddRange?() : Int32	public	Adds the elements of a array to the current Vector3List.
Clear() : Void	public	Removes all elements from the Vector3List.
Clone() : Object	public	Creates a shallow copy of the .
Contains() : Boolean	public	Determines whether a given is in the Vector3List.
CopyTo?() : Void	public	Copies the entire Vector3List to a one-dimensional array.
CopyTo?() : Void	public	Copies the entire Vector3List to a one-dimensional array, starting at the specified index of the target array.
GetEnumerator?() : IVector3ListEnumerator	public	Returns an enumerator that can iterate through the Vector3List.
IndexOf?() : Int32	public	Returns the zero-based index of the first occurrence of a in the Vector3List.
Insert() : Void	public	Inserts an element into the Vector3List at the specified index.
ReadOnly?() : Vector3List	public	Creates a read-only wrapper for a Vector3List instance.
Remove() : Void	public	Removes the first occurrence of a specific from the Vector3List.
RemoveAt?() : Void	public	Removes the element at the specified index of the Vector3List.
Synchronized() : Vector3List	public	Creates a synchronized (thread-safe) wrapper for a Vector3List instance.
TrimToSize?() : Void	public	Sets the capacity to the actual number of elements.

BaseCollection Class

Summary

public abstract class BaseCollection? : System.Collections.ICollection, System.Collections.IEnumerable, System.Collections.IEnumerator

Serves as a basis for strongly typed collections in the math lib.

Remarks

Can't wait for Generics in .Net Framework 2.0!

Constructor Members

Name	Access	Summary
BaseCollection?()	public

Field Members

Name	Access	Summary
objectList : ArrayList?	protected

Property Members

Name	Access	Summary
Count : Int32	public
Current : Object	public	Returns the current object in the enumeration.
IsSynchronized? : Boolean	public
Item : Object	public
SyncRoot? : Object	public

Method Members

Name	Access	Summary
Add() : Void	protected	Adds an item to the collection.
Clear() : Void	public	Clears all objects from the collection.
CopyTo?() : Void	public
GetEnumerator?() : IEnumerator	public
MoveNext?() : Boolean	public	Moves to the next item in the enumeration if there is one.
Remove() : Void	public	Removes the item from the collection.
Reset() : Void	public	Resets the in progress enumerator.

PlaneList Class

Summary

public class PlaneList? : ArrayList?, System.Collections.IList, System.Collections.ICollection, System.Collections.IEnumerable, System.ICloneable

Constructor Members

Name	Access	Summary
PlaneList?()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary

Method Members

Name	Access	Summary
Add() : Void	public

PlaneBoundedVolumeList Class

Summary

public class PlaneBoundedVolumeList? : ArrayList?, System.Collections.IList, System.Collections.ICollection, System.Collections.IEnumerable, System.ICloneable

Constructor Members

Name	Access	Summary
PlaneBoundedVolumeList?()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary

Method Members

Name	Access	Summary
Add() : Void	public

 

-- UpDown - 02 Feb 2007