Namespace List
The namespaces specified in this document are:
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
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. |
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
MathLib? Structs
Summary
public structure Vector2
2 dimensional vector.
Remarks
2 dimensional vector.
Constructor Members
Field Members
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. |
Summary
public structure Quaternion
Summary description for Quaternion.
Remarks
Summary description for Quaternion.
Constructor Members
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. |
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. |
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
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
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. |
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. |
Summary
public structure Vector4
4D homogeneous vector.
Remarks
4D homogeneous vector.
Constructor Members
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. |
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
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 produces the angle between them. |
| 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
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 |
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
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. |
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. |
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
Property Members
Coding Web