API Reference

Packed Record TGenericVector3

Description
Hierarchy
Nested Types
Fields
Methods
Properties

Unit

CastleVectorsInternalSingle

Declaration

type TGenericVector3 = packed record

Description

Vector of 3 floating-point values.

This is generic type (although not using "proper" Pascal generics for implementation reasons). In has two actual uses:

  1. TVector3, a vector of 3 Single values (floats with single precision),

  2. TVector3Double, a vector of 3 Double values (floats with double precision).

The actual type of TGenericScalar is Single or Double for (respectively) TVector3 or TVector3Double.

Overview

Nested Types

Public TIndex = 0..Count - 1;

Fields

Public nested const Count = 3;
Public X: TGenericScalar
Public Y: TGenericScalar
Public Z: TGenericScalar
Public Data: array [TIndex] of TGenericScalar
Public XY: TGenericVector2

Methods

Public class operator + (const A, B: TGenericVector3): TGenericVector3; inline;
Public class operator - (const A, B: TGenericVector3): TGenericVector3; inline;
Public class operator - (const V: TGenericVector3): TGenericVector3; inline;
Public class operator * (const V: TGenericVector3; const Scalar: TGenericScalar): TGenericVector3; inline;
Public class operator * (const Scalar: TGenericScalar; const V: TGenericVector3): TGenericVector3; inline;
Public class operator * (const V1, V2: TGenericVector3): TGenericVector3; inline;
Public class operator / (const V: TGenericVector3; const Scalar: TGenericScalar): TGenericVector3; inline;
Public procedure Init(const AX, AY, AZ: TGenericScalar); inline; deprecated 'initialize instead like "V := Vector3(X, Y, Z)"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.Init(X, Y, Z)"';
Public function ToString: string;
Public function ToRawString(const FloatFormat: String = '%g'): string;
Public function Normalize: TGenericVector3; inline;
Public procedure NormalizeMe; inline; deprecated 'normalize instead like "V := V.Normalize"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.NormalizeMe"';
Public function Length: TGenericScalar; inline;
Public function LengthSqr: TGenericScalar; inline;
Public function AdjustToLength(const NewLength: TGenericScalar): TGenericVector3; inline;
Public class function CrossProduct(const V1, V2: TGenericVector3): TGenericVector3; static; inline;
Public class function DotProduct(const V1, V2: TGenericVector3): TGenericScalar; static; inline;
Public function Abs: TGenericVector3; inline;
Public function Min: TGenericScalar;
Public function Max: TGenericScalar;
Public function Average: TGenericScalar; inline;
Public function IsZero: boolean; overload; inline;
Public function IsZero(const Epsilon: TGenericScalar): boolean; overload; inline;
Public function IsPerfectlyZero: boolean; inline;
Public class function Equals(const V1, V2: TGenericVector3): boolean; overload; inline; static;
Public class function Equals(const V1, V2: TGenericVector3; const Epsilon: TGenericScalar): boolean; overload; inline; static;
Public class function PerfectlyEquals(const V1, V2: TGenericVector3): boolean; static; inline;
Public class function Lerp(const A: TGenericScalar; const V1, V2: TGenericVector3): TGenericVector3; static; inline;
Public class function Zero: TGenericVector3; static; inline;

Properties

Public property AsArray [const Index: TIndex]: TGenericScalar read GetItems;
Public class property One [const Index: TIndex]: TGenericVector3 read GetOne;

Description

Nested Types

Public TIndex = 0..Count - 1;

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Fields

Public nested const Count = 3;

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Public X: TGenericScalar

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Public Y: TGenericScalar

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Public Z: TGenericScalar

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Public Data: array [TIndex] of TGenericScalar

Access (get, set) vector components by index.

Public XY: TGenericVector2

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Methods

Public class operator + (const A, B: TGenericVector3): TGenericVector3; inline;

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Public class operator - (const A, B: TGenericVector3): TGenericVector3; inline;

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Public class operator - (const V: TGenericVector3): TGenericVector3; inline;

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Public class operator * (const V: TGenericVector3; const Scalar: TGenericScalar): TGenericVector3; inline;

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Public class operator * (const Scalar: TGenericScalar; const V: TGenericVector3): TGenericVector3; inline;

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Public class operator * (const V1, V2: TGenericVector3): TGenericVector3; inline;

Vector * vector makes a component-wise multiplication. This is consistent with GLSL and other vector APIs.

Public class operator / (const V: TGenericVector3; const Scalar: TGenericScalar): TGenericVector3; inline;

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Public procedure Init(const AX, AY, AZ: TGenericScalar); inline; deprecated 'initialize instead like "V := Vector3(X, Y, Z)"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.Init(X, Y, Z)"';

Warning: this symbol is deprecated: initialize instead like "V := Vector3(X, Y, Z)"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.Init(X, Y, Z)"

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Public function ToString: string;

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Public function ToRawString(const FloatFormat: String = '%g'): string;

Convert to string using the most precise (not always easily readable by humans) float format. This may use the exponential (scientific) notation to represent the floating-point value, if needed.

You can pass, as parameter, the format to use. By default it is '%g', "general number format" with maximum precision documented on https://www.freepascal.org/docs-html/rtl/sysutils/format.html .

This is suitable for storing the value in a file, with a best precision possible.

Public function Normalize: TGenericVector3; inline;

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Public procedure NormalizeMe; inline; deprecated 'normalize instead like "V := V.Normalize"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.NormalizeMe"';

Warning: this symbol is deprecated: normalize instead like "V := V.Normalize"; modifying a temporary record value is a trap, e.g. this is not reliable: "Scene.Translation.NormalizeMe"

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Public function Length: TGenericScalar; inline;

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Public function LengthSqr: TGenericScalar; inline;

Vector length squared. This is slightly faster than Length as it avoids calculating a square root along the way. (But, please remember to not optimize your code without a need. Optimize only parts that are proven bottlenecks, otherwise don't make the code less readable for the sake of speed.)

Public function AdjustToLength(const NewLength: TGenericScalar): TGenericVector3; inline;

Calculate a new vector scaled so that it has length equal to NewLength. NewLength may be negative, in which case we'll negate the vector and then adjust it's length to Abs(NewLength).

Public class function CrossProduct(const V1, V2: TGenericVector3): TGenericVector3; static; inline;

Vector cross product. See http://en.wikipedia.org/wiki/Cross_product .

Result is a vector orthogonal to both given vectors. Generally there are two such vectors, this method returns the one following right-hand rule. More precisely, V1, V2 and Product(V1, V2) are in the same relation as basic X, Y, Z axes. Reverse the order of arguments to get negated result.

If you use this to calculate a normal vector of a triangle (P0, P1, P2): note that TVector3.CrossProduct(P1 - P0, P1 - P2) points out from CCW triangle side in right-handed coordinate system.

When V1 and V2 are parallel (that is, when V1 = V2 multiplied by some scalar), and this includes the case when one of them is zero, then result is a zero vector.

Public class function DotProduct(const V1, V2: TGenericVector3): TGenericScalar; static; inline;

Dot product of two vectors. See https://en.wikipedia.org/wiki/Dot_product .

Public function Abs: TGenericVector3; inline;

Absolute value on all components.

Public function Min: TGenericScalar;

Smallest component.

Public function Max: TGenericScalar;

Largest component.

Public function Average: TGenericScalar; inline;

Average from all components.

Public function IsZero: boolean; overload; inline;

Are all components equal to zero (within some epsilon margin).

Public function IsZero(const Epsilon: TGenericScalar): boolean; overload; inline;

Are all components equal to zero (within Epsilon margin).

Public function IsPerfectlyZero: boolean; inline;

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Public class function Equals(const V1, V2: TGenericVector3): boolean; overload; inline; static;

Compare two vectors, with epsilon to tolerate slightly different floats.

Public class function Equals(const V1, V2: TGenericVector3; const Epsilon: TGenericScalar): boolean; overload; inline; static;

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Public class function PerfectlyEquals(const V1, V2: TGenericVector3): boolean; static; inline;

Compare two vectors using exact comparison (like the "=" operator to compare floats).

Public class function Lerp(const A: TGenericScalar; const V1, V2: TGenericVector3): TGenericVector3; static; inline;

Linear interpolation between two vector values. Returns (1-A) * V1 + A * V2.

So:

  • A = 0 gives V1,

  • A = 1 gives V2,

  • values between are interpolated,

  • values outside are extrapolated.

Public class function Zero: TGenericVector3; static; inline;

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Properties

Public property AsArray [const Index: TIndex]: TGenericScalar read GetItems;

Get vector components by index. This is a default property, so you can write MyVector[0] instead of MyVector.Data[0] or MyVector.AsArray[0].

But note that this is not writeable (because exposing writeable properties on vectors would cause some subtle traps, see https://castle-engine.io/coding_traps ). Use MyVector.Data[0] := 123.456 if you want to set by index, or MyVector.X := 123.456.

Public class property One [const Index: TIndex]: TGenericVector3 read GetOne;

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