Create a 3d plane with three points

Question

We know a 3D plane is built by 3 points. Now in delphi I use GLScene there is a plane in which you cant see any arbitrary point to create a plan. My question is how to set a plane by 3 given points. According to SO rules I write my TGLPlane source code.

  TGLPlane = class(TGLSceneObject)
  private
    { Private Declarations }
    FXOffset, FYOffset: TGLFloat;
    FXScope, FYScope: TGLFloat;
    FWidth, FHeight: TGLFloat;
    FXTiles, FYTiles: Cardinal;
    FStyle: TGLPlaneStyles;
    FMesh: array of array of TVertexRec;
  protected
    { Protected Declarations }
    procedure SetHeight(const aValue: Single);
    procedure SetWidth(const aValue: Single);
    procedure SetXOffset(const Value: TGLFloat);
    procedure SetXScope(const Value: TGLFloat);
    function StoreXScope: Boolean;
    procedure SetXTiles(const Value: Cardinal);
    procedure SetYOffset(const Value: TGLFloat);
    procedure SetYScope(const Value: TGLFloat);
    function StoreYScope: Boolean;
    procedure SetYTiles(const Value: Cardinal);
    procedure SetStyle(const val: TGLPlaneStyles);

  public
    { Public Declarations }
    constructor Create(AOwner: TComponent); override;

    procedure Assign(Source: TPersistent); override;

    procedure BuildList(var rci: TRenderContextInfo); override;
    function GenerateSilhouette(const silhouetteParameters
      : TGLSilhouetteParameters): TGLSilhouette; override;

    function AxisAlignedDimensionsUnscaled: TVector; override;
    function RayCastIntersect(const rayStart, rayVector: TVector;
      intersectPoint: PVector = nil; intersectNormal: PVector = nil)
      : Boolean; override;
    { : Computes the screen coordinates of the smallest rectangle encompassing the plane.<p>
      Returned extents are NOT limited to any physical screen extents. }
    function ScreenRect(aBuffer: TGLSceneBuffer): TGLRect;

    { : Computes the signed distance to the point.<p>
      Point coordinates are expected in absolute coordinates. }
    function PointDistance(const aPoint: TVector): Single;

  published
    { Public Declarations }
    property Height: TGLFloat read FHeight write SetHeight;
    property Width: TGLFloat read FWidth write SetWidth;
    property XOffset: TGLFloat read FXOffset write SetXOffset;
    property XScope: TGLFloat read FXScope write SetXScope stored StoreXScope;
    property XTiles: Cardinal read FXTiles write SetXTiles default 1;
    property YOffset: TGLFloat read FYOffset write SetYOffset;
    property YScope: TGLFloat read FYScope write SetYScope stored StoreYScope;
    property YTiles: Cardinal read FYTiles write SetYTiles default 1;
    property Style: TGLPlaneStyles read FStyle write SetStyle
      default [psSingleQuad, psTileTexture];
  end;

Answer 1

In GLScene, a plane is determined by its position and direction, not directly by three points.

Let's label the points A, B, and C. Choose A to be the position. The cross product of vectors AB and AC will give you the normal vector. Use those results to set the plane's AbsolutePosition and AbsoluteDirection properties.