3D Dot Ball
lazarus / 39-Graphics

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Gigatron · 2025-05-13 19:06

Ok ,

3D Dot ball in perspective , don't know if it's correct, but i'am
trying to understand perspective
projection formula.

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i unit
Unit1; {$mode objfpc}{$H+} interface uses  Classes, SysUtils, Forms,
Controls, Graphics, Dialogs, ExtCtrls,  BGRAVirtualScreen, BGRABitmap,
BGRABitmapTypes; const  Rd = 230;//*2  Circ = 20;          // n
circle  DPerCircle = 30;    // dot / circle 30 if circle  PerspectiveZ
= 1000; type  TDots = record    x, y, z: Single;    clr: TBGRAPixel; 
end;   { TForm1 }   TForm1 = class(TForm)    BGRAVirtualScreen1:
TBGRAVirtualScreen;    Timer1: TTimer;    procedure FormCreate(Sender:
TObject);    procedure Timer1Timer(Sender: TObject);    procedure
BGRAVirtualScreen1Redraw(Sender: TObject; Bitmap: TBGRABitmap); 
private    FDots: array of TDots;    FX, FY: Single;  public 
end; var  Form1: TForm1; implementation {$R *.lfm} function
ClampByte(Value: Integer): Byte;begin  if Value < 0 then    Result :=
0  else if Value > 255 then    Result := 255  else    Result :=
Value;end; { TForm1 } procedure TForm1.FormCreate(Sender:
TObject);var  lat, lon: Integer;  phi, theta: Single;  y, r: Single; 
d: TDots;begin  SetLength(FDots, Circ * DPerCircle);  for lat := 0 to
Circ-1 do  begin    phi := (lat / (Circ - 1)) * Pi;    y := Cos(phi) *
Rd;    r := Sin(phi) * Rd+30; // premier cercle    for lon := 0 to
DPerCircle - 1 do    begin      theta := (lon / DPerCircle) * Pi * 2; 
    d.x := Cos(theta) * r;      d.y := y;      d.z := Sin(theta) * r; 
    d.clr := BGRA(255, 255, 0); // blanc      FDots[lat * DPerCircle +
lon] := d;    end;  end;  FX := 0;  FY := 0;end; procedure
TForm1.BGRAVirtualScreen1Redraw(Sender: TObject; Bitmap:
TBGRABitmap);var  dot: TDots;  x, y, z: Single;  rx, ry, rz: Single; 
cosX, sinX, cosY, sinY: Single;  scale: Single;  projX, projY:
Integer;  alpha: Byte;  sz: Single;begin  Bitmap.Fill(BGRABlack); 
cosX := Cos(FX); sinX := Sin(FX);  cosY := Cos(FY); sinY := Sin(FY);  
for dot in FDots do  begin    // Rotation X    x := dot.x;    y :=
dot.y * cosX - dot.z * sinX;    z := dot.y * sinX + dot.z * cosX;    
// Rotation Y    rx := x * cosY - z * sinY;    rz := x * sinY + z *
cosY;    ry := y;     // Projection    if (PerspectiveZ + rz) <> 0
then    begin      scale := PerspectiveZ / (PerspectiveZ + rz);     
projX := Round(Bitmap.Width / 2 + rx * scale);      projY :=
Round(Bitmap.Height / 2 + ry * scale);      sz := 2 * scale;     
alpha := ClampByte(Round(255 * (rz + Rd) / ( Rd/2)));     
Bitmap.FillEllipseAntialias(projX, projY, sz, sz, BGRA(255, 255, 255,
alpha));// or alpha    end;  end;end; procedure
TForm1.Timer1Timer(Sender: TObject);begin  FX += 0.008;  FY += 0.032; 
BGRAVirtualScreen1.RedrawBitmap;end; end.

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Dzandaa · 2025-05-15 15:43

Hi,

I don't know if that can help:

https://www.mauriciopoppe.com/notes/computer-
graphics/viewing/projection-transform/

B->

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Gigatron · 2025-05-15 20:15

Quote from: Dzandaa on May 15, 2025, 05:43:47 pmHi,

I don't know if that can help:

https://www.mauriciopoppe.com/notes/computer-
graphics/viewing/projection-transform/

B->

@Dzandaa Thank you very much , i will study this 3D projection, at the
moment x,y,z camera mat2 mat3  mat4 and 2drotation are easy for me,
the rest are for later

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TRon · 2025-05-15 20:37

@gigatron:
coding-train has a topic on drawing a 3d object onto a 2d screen here
with a brief explanation on perspective. In that video the host uses a
small trick for the perspective multiplication after the matrix
multiplications/rotation. It is a very simple solution only applicable
for the situation (so no camera and fov control).

Flipcode had a very nice article on that topic, step-by-step explained
in layman's terminology, but I seem unable to locate it

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Gigatron · 2025-05-15 22:37

Quote from: TRon on May 15, 2025, 10:37:50 pm@gigatron:
coding-train has a topic on drawing a 3d object onto a 2d screen here
with a brief explanation on perspective. In that video the host uses a
small trick for the perspective multiplication after the matrix
multiplications/rotation. It is a very simple solution only applicable
for the situation (so no camera and fov control).

Flipcode had a very nice article on that topic, step-by-step explained
in layman's terminology, but I seem unable to locate it 

Perfect explanation , thank you very much @Tron , i will try to
experiment this in pascal code a bit.