在Delphi的TImage控件上绘制球体

Question

我想画这样的球体:

下面的代码生成圆的顶点并在TIMAGE上绘制一个圆但我想要它用于SPHERE:

for i := 0 to 360 do begin 
   //Find value of X and Y 
   pntCordXY.X := Radius * Cos(DegToRad(i)); 
   pntCordXY.Y := Radius * Sin(DegToRad(i)); 
   if i = 0 then 
      image1.Canvas.MoveTo(Round(pntCordXY.X), Round(pntCordXY.Y)) 
   else 
      image1.Canvas.LineTo(Round(pntCordXY.X), Round(pntCordXY.Y)); 
end;

Answer 1

这结果是一个有趣的运动; 好问题!

首先,你专门要求在a上绘制这样的球体TImage,但该组件应该用于显示图形.当然,它有一个画布可以绘制,但在下面我使用一个TPaintBox是自己绘画的首选组件.因为,你必须自己画这个.完全.

需要的成分:

• 用于计算球体上的3D点,用于围绕多个轴旋转地球,以及用于将3D点转换为2D屏幕坐标系的一些数学计算.基础是:

  type
    TPoint3D = record
      X: Double;
      Y: Double;
      Z: Double;
    end;
  
  function Sphere(Phi, Lambda: Double): TPoint3D;
  begin
    Result.X := Cos(Phi) * Sin(Lambda);
    Result.Y := Sin(Phi);
    Result.Z := Cos(Phi) * Cos(Lambda);
  end;
  
  function RotateAroundX(const P: TPoint3D; Alfa: Double): TPoint3D;
  begin
    Result.X := P.X;
    Result.Y := P.Y * Cos(Alfa) + P.Z * Sin(Alfa);
    Result.Z := P.Y * -Sin(Alfa) + P.Z * Cos(Alfa);
  end;
  
  function RotateAroundY(const P: TPoint3D; Beta: Double): TPoint3D;
  begin
    Result.X := P.X * Cos(Beta) + P.Z * Sin(Beta);
    Result.Y := P.Y;
    Result.Z := P.X * -Sin(Beta) + P.Z * Cos(Beta);
  end;
  

• 一些全球变量可以使用:

  var
    Alfa: Integer;   //Rotation around X axis
    Beta: Integer;   //Rotation around Y axis
    C: TPoint;       //Center
    R: Integer;      //Radius
    Phi: Integer;    //Angle relative to XY plane
    Lambda: Integer; //Angle around Z axis (from pole to pole)
    P: TPoint3D;     //2D projection of a 3D point on the sphere's surface
  

• 用于计算纬度圈的所有点的代码:

  for Phi := -8 to 8 do
    for Lambda := 0 to 360 do
    begin
      P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
      P := RotateAroundX(P, Alfa);
      P := RotateAroundY(P, Beta);
    end;
  

• 用于计算经度经络的所有点的代码:

  for Lambda := 0 to 17 do
    for Phi := 0 to 360 do
    begin
      P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
      P := RotateAroundX(P, Alfa);
      P := RotateAroundY(P, Beta);
    end;
  

  These points can be used to draw lines or curves on the paint box. The Z value of these points are not used for drawing, but they are helpful to decide whether the point lies on the back or front side of the globe.

• Logic and aids. Before all points, lines or curves in front of the globe can be drawn, the ones in the back of globe have to be drawn first, in order to preserve depth.

• 绘图框架或绘图库.默认情况下,Delphi配备标准的Windows GDI,可通过Canvas颜料盒的属性获得.另一种可能性是GDI +,它更先进,更高效.特别是考虑反对.这些是我合作的两个框架,但也有其他框架.例如:OpenGL,它可以自动将3D对象转换为2D,并且能够添加3D表面,灯光,材质,着色器以及更多功能.

• 测试应用程序,在此问题的底部添加.

• 双缓冲技术,使油漆无闪烁.在绘制绘图框上的位图之前,我选择了一个单独的位图对象,在该对象上绘制了所有内容.演示程序还演示了没有它的性能(例程:) GDIMultipleColorsDirect.

建立:

掉落油漆盒窗体上,并将其设置为Align属性alClient,添加一个定时器组件进行仿真,添加表单事件处理程序OnCreate,OnDestroy,OnKeyPress,和OnResize,然后添加一个事件处理程序PaintBox1.OnPaint.

object Form1: TForm1
  Left = 497
  Top = 394
  Width = 450
  Height = 450
  Caption = 'Sphere'
  Color = clWhite
  Font.Charset = DEFAULT_CHARSET
  Font.Color = clWindowText
  Font.Height = -11
  Font.Name = 'MS Sans Serif'
  Font.Style = []
  OldCreateOrder = False
  OnCreate = FormCreate
  OnDestroy = FormDestroy
  OnKeyPress = FormKeyPress
  OnResize = FormResize
  PixelsPerInch = 96
  TextHeight = 13
  object PaintBox1: TPaintBox
    Left = 0
    Top = 0
    Width = 434
    Height = 414
    Align = alClient
    OnPaint = PaintBox1Paint
  end
  object Timer1: TTimer
    Interval = 25
    OnTimer = Timer1Timer
    Left = 7
    Top = 7
  end
end

第一次尝试:

使用默认的GDI,我从每个点到每个下一个点绘制线条.为了增加深度感(透视感),我给前面的线条增加了更大的宽度.此外,我逐渐让线条的颜色从暗到亮(例程:) GDIMultipleColors.

第二次尝试:

很好,但所有像素都很难!让我们尝试做一些反对自我的事情......;)此外,我将颜色数量减少到两个:前面是黑暗,后面是浅色.这是为了摆脱所有单独的线段:现在每个圆和子午线分成两条折线.我在其间使用了第三种颜色来防止反作用(例程:) GDIThreeColors.

GDI +救援:

这种反作用并不是最迷人的.为了获得非常流畅的绘画工作,让我们将代码转换为GDI +风格.对于Delphi 2009及更高版本,可从此处获取该库.对于较旧的Delphi版本,可从此处获取该库.

In GDI+, drawing works a bit differently. Create a TGPGraphics object and attach it to a device context with its constructor. Subsequently, drawing operations on the object are translated by the API and will be output to the destination context, the bitmap in this case (routine: GDIPlusDualLinewidths).

Can it even better?

Well, that's quite someting already. But this globe is made up out of polylines with just two different line widths. Let's add some in between. The count of segments in each circle or meridian is controlled by the Precision constant (routine: GDIPlusMultipleLinewidths).

Sample application:

Press a key to cycle through the above mentioned routines.

unit Globe;

interface

uses
  Windows, SysUtils, Classes, Graphics, Controls, Forms, ExtCtrls, Math,
  GDIPAPI, GDIPOBJ;

type
  TForm1 = class(TForm)
    PaintBox1: TPaintBox;
    Timer1: TTimer;
    procedure FormCreate(Sender: TObject);
    procedure FormDestroy(Sender: TObject);
    procedure FormResize(Sender: TObject);
    procedure Timer1Timer(Sender: TObject);
    procedure FormKeyPress(Sender: TObject; var Key: Char);
    procedure PaintBox1Paint(Sender: TObject);
  private
    FBmp: TBitmap;
    FPen: TGPPen;
    procedure GDIMultipleColorsDirect;
    procedure GDIMultipleColors;
    procedure GDIThreeColors;
    procedure GDIPlusDualLinewidths;
    procedure GDIPlusMultipleLinewidths;
  public
    A: Integer; //Alfa, rotation round X axis
    B: Integer; //Beta, rotation round Y axis
    C: TPoint;  //Center
    R: Integer; //Radius
  end;

var
  Form1: TForm1;

implementation

{$R *.DFM}

const
  LineColorFore = $00552B00;
  LineColorMiddle = $00AA957F;
  LineColorBack = $00FFDFBF;
  BackColor = clWhite;
  LineWidthFore = 4.5;
  LineWidthBack = 1.5;
  Precision = 10; //Should be even!

type
  TCycle = 0..Precision - 1;

  TPoint3D = record
    X: Double;
    Y: Double;
    Z: Double;
  end;

function Sphere(Phi, Lambda: Double): TPoint3D;
begin
  Result.X := Cos(Phi) * Sin(Lambda);
  Result.Y := Sin(Phi);
  Result.Z := Cos(Phi) * Cos(Lambda);
end;

function RotateAroundX(const P: TPoint3D; Alfa: Double): TPoint3D;
begin
  Result.X := P.X;
  Result.Y := P.Y * Cos(Alfa) + P.Z * Sin(Alfa);
  Result.Z := P.Y * -Sin(Alfa) + P.Z * Cos(Alfa);
end;

function RotateAroundY(const P: TPoint3D; Beta: Double): TPoint3D;
begin
  Result.X := P.X * Cos(Beta) + P.Z * Sin(Beta);
  Result.Y := P.Y;
  Result.Z := P.X * -Sin(Beta) + P.Z * Cos(Beta);
end;

{ TForm1 }

procedure TForm1.FormCreate(Sender: TObject);
begin
  Brush.Style := bsClear; //This is múch cheaper then DoubleBuffered := True
  FBmp := TBitmap.Create;
  FPen := TGPPen.Create(ColorRefToARGB(ColorToRGB(clBlack)));
  A := 35;
  B := 25;
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
  FPen.Free;
  FBmp.Free;
end;

procedure TForm1.FormResize(Sender: TObject);
begin
  C.X := PaintBox1.ClientWidth div 2;
  C.Y := PaintBox1.ClientHeight div 2;
  R := Min(C.X, C.Y) - 10;
  FBmp.Width := PaintBox1.ClientWidth;
  FBmp.Height := PaintBox1.ClientHeight;
end;

procedure TForm1.Timer1Timer(Sender: TObject);
begin
  A := A + 2;
  B := B + 1;
  PaintBox1.Invalidate;
end;

procedure TForm1.FormKeyPress(Sender: TObject; var Key: Char);
begin
  Tag := Tag + 1;
  PaintBox1.Invalidate;
end;

procedure TForm1.PaintBox1Paint(Sender: TObject);
begin
  case Tag mod 5 of
    0: GDIMultipleColorsDirect;
    1: GDIMultipleColors;
    2: GDIThreeColors;
    3: GDIPlusDualLinewidths;
    4: GDIPlusMultipleLinewidths;
  end;
end;

procedure TForm1.GDIPlusMultipleLinewidths;
var
  Lines: array of TPointFDynArray;
  PointCount: Integer;
  LineCount: Integer;
  Drawing: TGPGraphics;
  Alfa: Double;
  Beta: Double;
  Cycle: TCycle;
  Phi: Integer;
  Lambda: Integer;
  P: TPoint3D;
  Filter: TCycle;
  PrevFilter: TCycle;
  I: Integer;

  procedure ResetLines;
  begin
    SetLength(Lines, 0);
    LineCount := 0;
    PointCount := 0;
  end;

  procedure FinishLastLine;
  begin
    if PointCount < 2 then
      Dec(LineCount)
    else
      SetLength(Lines[LineCount - 1], PointCount);
  end;

  procedure NewLine;
  begin
    if LineCount > 0 then
      FinishLastLine;
    SetLength(Lines, LineCount + 1);
    SetLength(Lines[LineCount], 361);
    Inc(LineCount);
    PointCount := 0;
  end;

  procedure AddPoint(X, Y: Single);
  begin
    Lines[LineCount - 1][PointCount] := MakePoint(X, Y);
    Inc(PointCount);
  end;

  function CycleFromZ(Z: Single): TCycle;
  begin
    Result := Round((Z + 1) / 2 * High(TCycle));
  end;

  function CycleToLineWidth(ACycle: TCycle): Single;
  begin
    Result := LineWidthBack +
      (LineWidthFore - LineWidthBack) * (ACycle / High(TCycle));
  end;

  function CycleToLineColor(ACycle: TCycle): TGPColor;
  begin
    if ACycle <= (High(TCycle) div 2) then
      Result := ColorRefToARGB(ColorToRGB(LineColorBack))
    else
      Result := ColorRefToARGB(ColorToRGB(LineColorFore));
  end;

begin
  Drawing := TGPGraphics.Create(FBmp.Canvas.Handle);
  try
    Drawing.Clear(ColorRefToARGB(ColorToRGB(clWhite)));
    Drawing.SetSmoothingMode(SmoothingModeAntiAlias);
    Alfa := DegToRad(A);
    Beta := DegToRad(B);
    for Cycle := Low(TCycle) to High(TCycle) do
    begin
      ResetLines;
      //Latitude
      for Phi := -8 to 8 do
      begin
        NewLine;
        PrevFilter := 0;
        for Lambda := 0 to 360 do
        begin
          P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
          P := RotateAroundX(P, Alfa);
          P := RotateAroundY(P, Beta);
          Filter := CycleFromZ(P.Z);
          if Filter <> PrevFilter then
          begin
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
            NewLine;
          end;
          if Filter = Cycle then
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
          PrevFilter := Filter;
        end;
      end;
      //Longitude
      for Lambda := 0 to 17 do
      begin
        NewLine;
        PrevFilter := 0;
        for Phi := 0 to 360 do
        begin
          P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
          P := RotateAroundX(P, Alfa);
          P := RotateAroundY(P, Beta);
          Filter := CycleFromZ(P.Z);
          if Filter <> PrevFilter then
          begin
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
            NewLine;
          end;
          if Filter = Cycle then
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
          PrevFilter := Filter;
        end;
      end;
      FinishLastLine;
      FPen.SetColor(CycleToLineColor(Cycle));
      FPen.SetWidth(CycleToLineWidth(Cycle));
      for I := 0 to LineCount - 1 do
        Drawing.DrawLines(FPen, PGPPointF(@(Lines[I][0])), Length(Lines[I]));
      if Cycle = (High(TCycle) div 2 + 1) then
        Drawing.DrawEllipse(FPen, C.X - R, C.Y - R, 2 * R, 2 * R);
    end;
  finally
    Drawing.Free;
  end;
  PaintBox1.Canvas.Draw(0, 0, FBmp);
end;

procedure TForm1.GDIPlusDualLinewidths;
const
  LineColors: array[Boolean] of TColor = (LineColorFore, LineColorBack);
  LineWidths: array[Boolean] of Single = (LineWidthFore, LineWidthBack);
  BackColor = clWhite;
var
  Lines: array of TPointFDynArray;
  PointCount: Integer;
  LineCount: Integer;
  Drawing: TGPGraphics;
  Alfa: Double;
  Beta: Double;
  Phi: Integer;
  Lambda: Integer;
  BackSide: Boolean;
  P: TPoint3D;
  PrevZ: Double;
  I: Integer;

  procedure ResetLines;
  begin
    SetLength(Lines, 0);
    LineCount := 0;
    PointCount := 0;
  end;

  procedure FinishLastLine;
  begin
    if PointCount < 2 then
      Dec(LineCount)
    else
      SetLength(Lines[LineCount - 1], PointCount);
  end;

  procedure NewLine;
  begin
    if LineCount > 0 then
      FinishLastLine;
    SetLength(Lines, LineCount + 1);
    SetLength(Lines[LineCount], 361);
    Inc(LineCount);
    PointCount := 0;
  end;

  procedure AddPoint(X, Y: Single);
  begin
    Lines[LineCount - 1][PointCount] := MakePoint(X, Y);
    Inc(PointCount);
  end;

begin
  Drawing := TGPGraphics.Create(FBmp.Canvas.Handle);
  try
    Drawing.Clear(ColorRefToARGB(ColorToRGB(clWhite)));
    Drawing.SetSmoothingMode(SmoothingModeAntiAlias);
    Alfa := DegToRad(A);
    Beta := DegToRad(B);
    for BackSide := True downto False do
    begin
      ResetLines;
      //Latitude
      for Phi := -8 to 8 do
      begin
        NewLine;
        PrevZ := 0;
        for Lambda := 0 to 360 do
        begin
          P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
          P := RotateAroundX(P, Alfa);
          P := RotateAroundY(P, Beta);
          if Sign(P.Z) <> Sign(PrevZ) then
            NewLine;
          if (BackSide and (P.Z < 0)) or (not BackSide and (P.Z >= 0)) then
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
          PrevZ := P.Z;
        end;
      end;
      //Longitude
      for Lambda := 0 to 17 do
      begin
        NewLine;
        PrevZ := 0;
        for Phi := 0 to 360 do
        begin
          P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
          P := RotateAroundX(P, Alfa);
          P := RotateAroundY(P, Beta);
          if Sign(P.Z) <> Sign(PrevZ) then
            NewLine;
          if (BackSide and (P.Z < 0)) or (not BackSide and (P.Z >= 0)) then
            AddPoint(C.X + P.X * R, C.Y + P.Y * R);
          PrevZ := P.Z;
        end;
      end;
      FinishLastLine;
      FPen.SetColor(ColorRefToARGB(ColorToRGB(LineColors[BackSide])));
      FPen.SetWidth(LineWidths[BackSide]);
      for I := 0 to LineCount - 1 do
        Drawing.DrawLines(FPen, PGPPointF(@(Lines[I][0])), Length(Lines[I]));
    end;
    Drawing.DrawEllipse(FPen, C.X - R, C.Y - R, 2 * R, 2 * R);
  finally
    Drawing.Free;
  end;
  PaintBox1.Canvas.Draw(0, 0, FBmp);
end;

procedure TForm1.GDIThreeColors;
const
  LineColors: array[TValueSign] of TColor = (LineColorBack, LineColorMiddle,
    LineColorFore);
  LineWidths: array[TValueSign] of Integer = (2, 4, 2);
var
  Lines: array of array of TPoint;
  PointCount: Integer;
  LineCount: Integer;
  Alfa: Double;
  Beta: Double;
  Phi: Integer;
  Lambda: Integer;
  BackSide: Boolean;
  P: TPoint3D;
  PrevZ: Double;
  I: TValueSign;
  J: Integer;

  procedure ResetLines;
  begin
    SetLength(Lines, 0);
    LineCount := 0;
    PointCount := 0;
  end;

  procedure FinishLastLine;
  begin
    if PointCount < 2 then
      Dec(LineCount)
    else
      SetLength(Lines[LineCount - 1], PointCount);
  end;

  procedure NewLine;
  begin
    if LineCount > 0 then
      FinishLastLine;
    SetLength(Lines, LineCount + 1);
    SetLength(Lines[LineCount], 361);
    Inc(LineCount);
    PointCount := 0;
  end;

  procedure AddPoint(APoint: TPoint); overload;
  var
    Last: TPoint;
  begin
    if PointCount > 0 then
    begin
      Last := Lines[LineCount - 1][PointCount - 1];
      if (APoint.X = Last.X) and (APoint.Y = Last.Y) then
        Exit;
    end;
    Lines[LineCount - 1][PointCount] := APoint;
    Inc(PointCount);
  end;

  procedure AddPoint(X, Y: Integer); overload;
  begin
    AddPoint(Point(X, Y));
  end;

begin
  FBmp.Canvas.Brush.Color := BackColor;
  FBmp.Canvas.FillRect(Rect(0, 0, FBmp.Width, FBmp.Height));
  Alfa := DegToRad(A);
  Beta := DegToRad(B);
  for BackSide := True downto False do
  begin
    ResetLines;
    //Latitude
    for Phi := -8 to 8 do
    begin
      NewLine;
      PrevZ := 0;
      for Lambda := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if Sign(P.Z) <> Sign(PrevZ) then
          NewLine;
        if (BackSide and (P.Z < 0)) or (not BackSide and (P.Z >= 0)) then
          AddPoint(Round(C.X + P.X * R), Round(C.Y + P.Y * R));
        PrevZ := P.Z;
      end;
    end;
    //Longitude
    for Lambda := 0 to 17 do
    begin
      NewLine;
      PrevZ := 0;
      for Phi := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if Sign(P.Z) <> Sign(PrevZ) then
          NewLine;
        if (BackSide and (P.Z < 0)) or (not BackSide and (P.Z >= 0)) then
          AddPoint(Round(C.X + P.X * R), Round(C.Y + P.Y * R));
        PrevZ := P.Z;
      end;
    end;
    FinishLastLine;
    if BackSide then
    begin
      FBmp.Canvas.Pen.Color := LineColors[-1];
      FBmp.Canvas.Pen.Width := LineWidths[-1];
      for J := 0 to LineCount - 1 do
        FBmp.Canvas.Polyline(Lines[J]);
    end
    else
      for I := 0 to 1 do
      begin
        FBmp.Canvas.Pen.Color := LineColors[I];
        FBmp.Canvas.Pen.Width := LineWidths[I];
        for J := 0 to LineCount - 1 do
          FBmp.Canvas.Polyline(Lines[J])
      end
  end;
  FBmp.Canvas.Brush.Style := bsClear;
  FBmp.Canvas.Ellipse(C.X - R, C.Y - R, C.X + R, C.Y + R);
  PaintBox1.Canvas.Draw(0, 0, FBmp);
end;

procedure TForm1.GDIMultipleColors;
var
  Alfa: Double;
  Beta: Double;
  Phi: Integer;
  Lambda: Integer;
  P: TPoint3D;
  Backside: Boolean;

  function ColorFromZ(Z: Single): TColorRef;
  var
    R: Integer;
    G: Integer;
    B: Integer;
  begin
    Z := (Z + 1) / 2;
    R := GetRValue(LineColorFore) - GetRValue(LineColorBack);
    R := GetRValue(LineColorBack) + Round(Z * R);
    G := GetGValue(LineColorFore) - GetGValue(LineColorBack);
    G := GetGValue(LineColorBack) + Round(Z * G);
    B := GetBValue(LineColorFore) - GetBValue(LineColorBack);
    B := GetBValue(LineColorBack) + Round(Z * B);
    Result := RGB(R, G, B);
  end;

begin
  FBmp.Canvas.Pen.Width := 2;
  FBmp.Canvas.Brush.Color := BackColor;
  FBmp.Canvas.FillRect(PaintBox1.ClientRect);
  Alfa := DegToRad(A);
  Beta := DegToRad(B);
  for Backside := True downto False do
  begin
    if not BackSide then
      FBmp.Canvas.Pen.Width := 3;
    //Latitude
    for Phi := -8 to 8 do
      for Lambda := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if (Lambda = 0) or (Backside and (P.Z >= 0)) or
          (not Backside and (P.Z < 0)) then
            FBmp.Canvas.MoveTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R))
        else
        begin
          FBmp.Canvas.Pen.Color := ColorFromZ(P.Z);
          FBmp.Canvas.LineTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R));
        end;
      end;
    //Longitude
    for Lambda := 0 to 17 do
      for Phi := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if (Phi = 0) or (Backside and (P.Z >= 0)) or
          (not Backside and (P.Z < 0)) then
            FBmp.Canvas.MoveTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R))
        else
        begin
          FBmp.Canvas.Pen.Color := ColorFromZ(P.Z);
          FBmp.Canvas.LineTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R));
        end;
      end;
  end;
  PaintBox1.Canvas.Draw(0, 0, FBmp);
end;

procedure TForm1.GDIMultipleColorsDirect;
var
  Alfa: Double;
  Beta: Double;
  Phi: Integer;
  Lambda: Integer;
  P: TPoint3D;
  Backside: Boolean;

  function ColorFromZ(Z: Single): TColorRef;
  var
    R: Integer;
    G: Integer;
    B: Integer;
  begin
    Z := (Z + 1) / 2;
    R := GetRValue(LineColorFore) - GetRValue(LineColorBack);
    R := GetRValue(LineColorBack) + Round(Z * R);
    G := GetGValue(LineColorFore) - GetGValue(LineColorBack);
    G := GetGValue(LineColorBack) + Round(Z * G);
    B := GetBValue(LineColorFore) - GetBValue(LineColorBack);
    B := GetBValue(LineColorBack) + Round(Z * B);
    Result := RGB(R, G, B);
  end;

begin
  PaintBox1.Canvas.Pen.Width := 2;
  PaintBox1.Canvas.Brush.Color := BackColor;
  PaintBox1.Canvas.FillRect(PaintBox1.ClientRect);
  Alfa := DegToRad(A);
  Beta := DegToRad(B);
  for Backside := True downto False do
  begin
    if not BackSide then
      PaintBox1.Canvas.Pen.Width := 3;
    //Latitude
    for Phi := -8 to 8 do
      for Lambda := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi * 10), DegToRad(Lambda));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if (Lambda = 0) or (Backside and (P.Z >= 0)) or
          (not Backside and (P.Z < 0)) then
            PaintBox1.Canvas.MoveTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R))
        else
        begin
          PaintBox1.Canvas.Pen.Color := ColorFromZ(P.Z);
          PaintBox1.Canvas.LineTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R));
        end;
      end;
    //Longitude
    for Lambda := 0 to 17 do
      for Phi := 0 to 360 do
      begin
        P := Sphere(DegToRad(Phi), DegToRad(Lambda * 10));
        P := RotateAroundX(P, Alfa);
        P := RotateAroundY(P, Beta);
        if (Phi = 0) or (Backside and (P.Z >= 0)) or
          (not Backside and (P.Z < 0)) then
            PaintBox1.Canvas.MoveTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R))
        else
        begin
          PaintBox1.Canvas.Pen.Color := ColorFromZ(P.Z);
          PaintBox1.Canvas.LineTo(C.X + Round(P.X * R), C.Y + Round(P.Y * R));
        end;
      end;
  end;
end;

end.

(With thanks to bummi's comment.)