画贝塞尔曲线

在Delph下调用PolyBezier();
procedure TForm1.Button1Click(Sender: TObject);
var point:array[0..6] of Tpoint;
    h:HDC;
begin
h:=getdc(form1.handle);
point[0].x:=25; point[0].y:=25;
point[1].x:=35; point[1].y:=170;
point[2].x:=130;point[2].y:=120;
point[3].x:=150;point[3].y:=150;
point[4].x:=170;point[4].y:=280;
point[5].x:=250;point[5].y:=115;
point[6].x:=250;point[6].y:=225;
polybezier(h,point,7);
end;

PolyBezier 画一系列相连的曲线，每一段包含4个point，第一点是曲线起点，
第二点，第三点指定曲线形状的控制点，第四点是曲线终点。
本例中，1为起点，4为中点，7为终点，2，3，5，6为控制点。
OR 调用canvas.polybezier();

*** Drawing CURVES in Delphi? ***
Solution 1
From: dmitrys@phyast.la.asu.edu (Dmitry Streblechenko)

In article <4uijv6$kf7@newsbf02.news.aol.com,
   gtabsoft2@aol.com (GTABSoft2) wrote:
Does anyone have source code or info on drawing Bezier curves? I must have
it for my component. Please respond to my email address.
I did this some time ago; I was too lazy to learn how to draw Bezier curves using Win API, so I did it using Polyline().

Note I used floating type values for points coordinates, (I used some kind of virtual screen), just change them to integer.

--------------------------------------------------------------------------------

 PBezierPoint = ^TBezierPoint;
 TBezierPoint = record
  X,Y:double;   //main node
  Xl,Yl:double; //left control point
  Xr,Yr:double; //right control point
 end;

//P1 and P2 are two TBezierPoint's, t is between 0 and 1:
//when t=0 X=P1.X, Y=P1.Y; when t=1 X=P2.X, Y=P2.Y;

procedure BezierValue(P1,P2:TBezierPoint; t:double; var X,Y:double);
 var t_sq,t_cb,r1,r2,r3,r4:double;
 begin
     t_sq := t * t;
     t_cb := t * t_sq;
     r1 := (1 - 3*t + 3*t_sq -   t_cb)*P1.X;
     r2 := (    3*t - 6*t_sq + 3*t_cb)*P1.Xr;
     r3 := (          3*t_sq - 3*t_cb)*P2.Xl;
     r4 := (                     t_cb)*P2.X;
     X  := r1 + r2 + r3 + r4;
     r1 := (1 - 3*t + 3*t_sq -   t_cb)*P1.Y;
     r2 := (    3*t - 6*t_sq + 3*t_cb)*P1.Yr;
     r3 := (          3*t_sq - 3*t_cb)*P2.Yl;
     r4 := (                     t_cb)*P2.Y;
     Y  := r1 + r2 + r3 + r4;
 end;

--------------------------------------------------------------------------------

To draw Bezier curve, split interval between P1 and P2 into several intervals based on how coarse you want your Bezier curve look (3 - 4 pixels looks Ok), then in a loop create an array of points using procedure above with t from 0 to 1 and draw that array of points using polyline().

Solution 2
From: saconn@iol.ie (Stephen Connolly)

gtabsoft2@aol.com (GTABSoft2) wrote:
Does anyone have source code or info on drawing Bezier curves? I must have
it for my component. Please respond to my email address.
I'm posting this here - 'cause: 1. I've seen people ask for this before, 2. The reference is so old I just had to. (BTW I have older references than this ;-P)

I'm sure that there is a standard Borland disclaimer to go with this:

--------------------------------------------------------------------------------

(********************************************************************)
(*                         GRAPHIX TOOLBOX 4.0                      *)
(*       Copyright (c) 1985, 87 by  Borland International, Inc.     *)
(********************************************************************)
unit GShell;

interface

{-------------------------------- snip ----------------------------}

procedure Bezier(A : PlotArray; MaxContrPoints : integer;
                 var B : PlotArray; MaxIntPoints : integer);

implementation

{-------------------------------- snip ---------------------------}

procedure Bezier{(A : PlotArray; MaxContrPoints : integer;
                 var B : PlotArray; MaxIntPoints : integer)};
const
  MaxControlPoints = 25;
type
  CombiArray = array[0..MaxControlPoints] of Float;
var
  N : integer;
  ContrPoint, IntPoint : integer;
  T, SumX, SumY, Prod, DeltaT, Quot : Float;
  Combi : CombiArray;

begin
  MaxContrPoints := MaxContrPoints - 1;
  DeltaT := 1.0 / (MaxIntPoints - 1);
  Combi[0] := 1;
  Combi[MaxContrPoints] := 1;
  for N := 0 to MaxContrPoints - 2 do
    Combi[N + 1] := Combi[N] * (MaxContrPoints - N) / (N + 1);
  for IntPoint := 1 to MaxIntPoints do
  begin
    T := (IntPoint - 1) * DeltaT;
    if T <= 0.5 then
      begin
        Prod := 1.0 - T;
        Quot := Prod;
        for N := 1 to MaxContrPoints - 1 do
          Prod := Prod * Quot;
        Quot := T / Quot;
        SumX := A[MaxContrPoints + 1, 1];
        SumY := A[MaxContrPoints + 1, 2];
        for N := MaxContrPoints downto 1 do
        begin
          SumX := Combi[N - 1] * A[N, 1] + Quot * SumX;
          SumY := Combi[N - 1] * A[N, 2] + Quot * SumY;
        end;
      end
    else
      begin
        Prod := T;
        Quot := Prod;
        for N := 1 to MaxContrPoints - 1 do
          Prod := Prod * Quot;
        Quot := (1 - T) / Quot;
        SumX := A[1, 1];
        SumY := A[1, 2];
        for N := 1 to MaxContrPoints do
        begin
          SumX := Combi[N] * A[N + 1, 1] + Quot * SumX;
          SumY := Combi[N] * A[N + 1, 2] + Quot * SumY;
        end;
      end;
    B[IntPoint, 1] := SumX * Prod;
    B[IntPoint, 2] := SumY * Prod;
  end;
end; { Bezier }

end. { GShell }