interface
#
Scientific.Core.IRealFunction
IRealFunction = interface
end
Represents a real-valued function $f\colon\mathbb{R}\to\mathbb{R}$.
Unit
Scientific.Core
Declared in Scientific.Core.pas
Defines geometric primitives and scalar-function abstractions. Vectors use Cartesian coordinates:
$$
\mathbf{v} = \begin{bmatrix}v_x \\ v_y\end{bmatrix} \in \mathbb{R}^2.
$$
Interface dependencies
0None.
Types
3class
#
Scientific.Core.TRealFunction
Relationships:
- Inherits from
TInterfacedObject - Implements
IRealFunction
TRealFunction = class(TInterfacedObject, IRealFunction)
end
Supplies reference counting for concrete real-valued functions.
record
#
Scientific.Core.TVector2
TVector2 = record
end
Stores a vector $\mathbf{v}=(v_x,v_y)$ in the Euclidean plane.
Routines
7routine
#
Scientific.Core.AngleBetween
function AngleBetween(const A: TVector2; const B: TVector2): Double
Measures the unsigned angle between two non-zero vectors.
$$
\theta=\arccos\!\left(
\frac{\mathbf{a}\cdot\mathbf{b}}
{\lVert\mathbf{a}\rVert_2\lVert\mathbf{b}\rVert_2}
\right).
$$
Parameters
| Name | Description |
|---|---|
A | First vector $\mathbf{a}$. |
B | Second vector $\mathbf{b}$. |
Returns
The angle $\theta\in[0,\pi]$, or zero for a zero input.
routine
#
Scientific.Core.Distance
function Distance(const A: TVector2; const B: TVector2): Double
Computes the distance between two points.
$$
d(\mathbf{a},\mathbf{b})=\lVert\mathbf{a}-\mathbf{b}\rVert_2.
$$
Parameters
| Name | Description |
|---|---|
A | First point $\mathbf{a}$. |
B | Second point $\mathbf{b}$. |
Returns
Their Euclidean distance.
routine
#
Scientific.Core.Dot
function Dot(const A: TVector2; const B: TVector2): Double
Computes the Euclidean inner product.
$$
\mathbf{a}\cdot\mathbf{b}=a_xb_x+a_yb_y.
$$
Parameters
| Name | Description |
|---|---|
A | Left vector $\mathbf{a}$. |
B | Right vector $\mathbf{b}$. |
Returns
The scalar inner product.
routine
#
Scientific.Core.Magnitude
function Magnitude(const Value: TVector2): Double
Computes the Euclidean magnitude of a vector.
$$
\lVert\mathbf{v}\rVert_2=\sqrt{v_x^2+v_y^2}.
$$
Parameters
| Name | Description |
|---|---|
Value | Vector $\mathbf{v}$. |
Returns
Its non-negative magnitude.
routine
#
Scientific.Core.Normalize
function Normalize(const Value: TVector2): TVector2
Produces a unit vector with the same direction.
$$
\widehat{\mathbf{v}}=
\frac{\mathbf{v}}{\lVert\mathbf{v}\rVert_2}.
$$
The zero vector maps to itself rather than dividing by zero.
Parameters
| Name | Description |
|---|---|
Value | Vector $\mathbf{v}$ to normalize. |
Returns
$\widehat{\mathbf{v}}$ or $(0,0)$ for a zero input.
routine
#
Scientific.Core.Rotate
function Rotate(const Value: TVector2; const Angle: Double): TVector2
Rotates a vector counter-clockwise by $\theta$ radians.
$$
R(\theta)=
\begin{bmatrix}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta
\end{bmatrix},
\qquad \mathbf{v}'=R(\theta)\mathbf{v}.
$$
Parameters
| Name | Description |
|---|---|
Value | Vector $\mathbf{v}$ to rotate. |
Angle | Rotation angle $\theta$ in radians. |
Returns
The rotated vector $\mathbf{v}'$.
routine
#
Scientific.Core.Vector2
function Vector2(const X: Double; const Y: Double): TVector2
Constructs the vector $\mathbf{v}=(x,y)$.
Parameters
| Name | Description |
|---|---|
X | Horizontal component $v_x$. |
Y | Vertical component $v_y$. |
Returns
A vector containing both components.
Members
4method
#
Scientific.Core.IRealFunction.Evaluate
Parent: Scientific.Core.IRealFunction
function Evaluate(const X: Double): Double
Evaluates $f(x)$ at one real argument.
Parameters
| Name | Description |
|---|---|
X | Argument supplied to the function. |
Returns
The scalar value $f(X)$.
method
#
Scientific.Core.TRealFunction.Evaluate
Parent: Scientific.Core.TRealFunction
function Evaluate(const X: Double): Double; virtual; abstract
Evaluates the concrete function at $x$.
Parameters
| Name | Description |
|---|---|
X | Argument supplied to the function. |
Returns
The scalar value $f(X)$.
field
#
Scientific.Core.TVector2.X
Parent: Scientific.Core.TVector2
X : Double
Horizontal component $v_x$.
field
#
Scientific.Core.TVector2.Y
Parent: Scientific.Core.TVector2
Y : Double
Vertical component $v_y$.