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elements.pas
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elements.pas
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(******************************************************************************)
(* *)
(* Author : Uwe Schächterle (Corpsman) *)
(* *)
(* This file is part of example PingPong *)
(* *)
(* See the file license.md, located under: *)
(* https://github.com/PascalCorpsman/Software_Licenses/blob/main/license.md *)
(* for details about the license. *)
(* *)
(* It is not allowed to change or remove this text from any *)
(* source file of the project. *)
(* *)
(******************************************************************************)
Unit elements;
{$MODE ObjFPC}{$H+}
Interface
Uses
classes, math,
LCLIntf, LCLType, // LMessages, // Trect
graphics; // TCanvas, TColor
Type
TBall = Class;
TFpoint = Record
x, y: Single;
End;
TBall = Class
private
fvx, fvy, fx, fy, fr, fm: Single;
fc: Tcolor;
Function getpos: Tfpoint;
Procedure Setpos(Value: TFpoint);
Function getSpeed: Tfpoint;
Procedure SetSpeed(Value: TFpoint);
public
Property Color: Tcolor read FC write fC;
Property Radius: Single read fr;
Property Position: Tfpoint read getpos write Setpos;
Property SpeedVektor: TFpoint read getSpeed write SetSpeed;
Property Mass: Single read Fm write fm;
Constructor Create(Position_, SpeedVektor_: TFpoint; Radius_, Mass_: single);
Destructor Destroy; override;
Procedure Render(Const Canvas: TCanvas);
Procedure CalculateMass;
Procedure BorderCollision(CollisionRect: Trect; InsideCollision: Boolean = True);
Procedure CollideWithOther(Const Ball2: TBall);
Procedure Move;
End;
Function Point(x, y: Single): Tfpoint;
Function Rect(ALeft, ATop, ARight, ABottom: Integer): Trect;
Implementation
Function Point(x, y: Single): Tfpoint;
Begin
result.x := x;
result.y := y;
End;
Function Rect(ALeft, ATop, ARight, ABottom: Integer): Trect;
Begin
With result Do Begin
Left := aleft;
Right := aright;
Top := atop;
bottom := abottom;
End;
End;
Constructor Tball.Create(Position_, SpeedVektor_: TFpoint; Radius_, Mass_: single);
Begin
Inherited Create;
fc := Random(256 * 256 * 256); // zufällige Farbe für unsere Kugel.
fx := position_.x;
fy := position_.y;
fr := radius_;
fm := mass_;
fvx := SpeedVektor_.x;
fvy := SpeedVektor_.y;
End;
Destructor Tball.Destroy;
Begin
// Inherited Destroy; // Brauchen wir net da von Tobject abgeleitet
End;
Function Tball.getpos: Tfpoint;
Begin
result.x := fx;
result.y := fy;
End;
Procedure Tball.Setpos(Value: TFpoint);
Begin
fx := value.x;
fy := value.y;
End;
Function Tball.getSpeed: Tfpoint;
Begin
result.x := fVx;
result.y := fVy;
End;
Procedure Tball.SetSpeed(Value: TFpoint);
Begin
fvx := value.x;
fvy := value.y;
End;
Procedure Tball.move;
Begin
fx := fx + fvx;
fy := fy + fvy;
End;
Function Tangens(Value: Extended): Extended;
Begin
result := tan(degtorad(value));
End;
Function Sinus(E: Extended): Extended;
Begin
Result := sin(degtorad(e));
End;
Function CoSinus(E: Extended): Extended;
Begin
Result := cos(degtorad(e));
End;
Procedure Tausche(Var i1, i2: integer);
Var
i3: integer;
Begin
i3 := i1;
i1 := i2;
i2 := i3;
End;
Function arcTangens(x, y: Extended): Extended;
Begin
Result := 0;
If (x = 0) Then Begin
If (Y >= 0) Then result := 90;
If (Y < 0) Then result := 270;
End
Else Begin
result := radtodeg(arctan(Y / X));
If ((X < 0) And (y > 0)) Or ((x < 0) And (Y <= 0)) Then result := 180 + result;
If (X > 0) And (Y < 0) Then result := 360 + result;
End;
End;
Function EllipseRechteckcollision(E1, R1: Trect): boolean;
Type
Tpunkt = Record
X, Y: Extended;
End;
Var
SN1, SN2, X, Alpha: extended;
p1, p2: Tpoint;
N1, N2: Tpunkt;
radius1, radius2: integer;
Begin
result := false;
If E1.left > E1.right Then tausche(E1.left, E1.right);
If E1.Top > E1.bottom Then tausche(E1.top, E1.bottom);
If r1.left > r1.right Then tausche(r1.left, r1.right);
If r1.Top > r1.bottom Then tausche(r1.top, r1.bottom);
p1.x := E1.left + ((E1.right - E1.left) Div 2);
p1.y := E1.top + ((E1.Bottom - E1.top) Div 2);
p2.x := r1.left + ((r1.right - r1.left) Div 2);
p2.y := r1.top + ((r1.Bottom - r1.top) Div 2);
Alpha := arcTangens(p1.x - p2.x, p1.y - p2.y);
X := Hypot(p1.x - p2.x, p1.y - p2.y);
Radius1 := p1.x - E1.left;
Radius2 := p1.y - E1.top; // Radius 1 Horizontal, Radius2 Vertikal
N1.X := cosinus(alpha) * radius1 + P1.X;
N1.Y := sinus(Alpha) * radius2 + P1.Y;
SN1 := Hypot(p1.x - n1.x, p1.y - n1.y);
Case round(Alpha) Of
0..45: Begin
n2.x := R1.right;
n2.y := round(tangens(alpha) * ((r1.Bottom - p2.y) / 2)) + p2.y;
End;
46..90: Begin
n2.y := R1.top;
n2.x := round(tangens(alpha - 45) * ((r1.right - p2.x) / 2)) + p2.x;
End;
91..135: Begin
n2.y := R1.top;
n2.x := round(tangens(alpha - 90) * ((r1.right - p2.x) / 2)) + p2.x;
End;
136..225: Begin
n2.x := r1.left;
n2.y := round(tangens(alpha) * ((r1.Bottom - p2.y) / 2)) + p2.y;
End;
226..270: Begin
n2.y := r1.bottom;
n2.x := round(tangens(alpha - 225) * ((r1.right - p2.x) / 2)) + p2.x;
End;
271..315: Begin
n2.y := r1.bottom;
n2.x := round(tangens(alpha - 270) * ((r1.right - p2.x) / 2)) + p2.x;
End;
316..360: Begin
n2.x := R1.right;
n2.y := round(tangens(alpha) * ((r1.Bottom - p2.y) / 2)) + p2.y;
End;
End;
SN2 := Hypot(p2.x - n2.x, p2.y - n2.y);
If (x <= (sn1 + Sn2)) Then result := true;
End;
Procedure Tball.BorderCollision(CollisionRect: Trect; InsideCollision: Boolean = True);
Begin
If Insidecollision Then Begin // Bedeutet die Kugel befindet sich inherhalt des Rechtecks
If ((fx - fr < CollisionRect.Left) And (fvx < 0)) Or ((fx + fr > CollisionRect.Right) And (fvx > 0)) Then fvx := -fvx;
If ((fy - fr < CollisionRect.top) And (fvy < 0)) Or ((fy + fr > CollisionRect.Bottom) And (fvy > 0)) Then fvy := -fvy;
End
Else Begin // bedeutet die Kugel befindet sich auserhalb des Rechtecks
If EllipseRechteckcollision(rect(round(fx - fr), round(fy - fr), round(fx + fr), round(fy + fr)), CollisionRect) Then Begin
If ((fy < CollisionRect.top) And (fvy > 0)) Or ((fy > CollisionRect.Bottom) And (fvy < 0)) Then fvy := -fvy;
If ((fx < CollisionRect.left) And (fvx > 0)) Or ((fx > CollisionRect.Right) And (fvx < 0)) Then fvx := -fvx;
End;
End;
End;
Procedure Tball.CollideWithOther(Const Ball2: TBall);
Var
dx, dy, dxs, dys, L, // Die Variablen für den Abstand der beiden Kugeln
M11, M21, M12, M22, // Die Variablen der Transformationsmatrix
Vp1, Vp2, Vs1, Vs2, MTot, Vp1_, Vp2_: Single;
tmpv: TFpoint;
Begin
tmpv := ball2.Position; // Hohlen der position der anderen Kugel
DX := tmpv.x - fx; // Delta x
DY := tmpv.y - fy; // Delta y
dxs := dx * dx; // Da wir ein wenig Zeitoptimiert arbeiten wollen speichern wir und die Quadrate zwischen
dys := dy * dy; // Da wir ein wenig Zeitoptimiert arbeiten wollen speichern wir und die Quadrate zwischen
l := fr + ball2.Radius; // die Strecke der beiden Radien Addiert
// da l * l bestimmt schneller ist wie Wurzel ziehen machen wir das so, unter der Annahme das es möglichst selten eine Kollision gibt.
// Im anderen Fall wäre die Berechnung von L vor dem If und dem Vergleich auf tr schneller.
If dxs + dys <= l * l Then Begin
L := sqrt(dxs + dys); // Abstand
// Berechnen der Transformationsmatrix
M11 := DX / L;
M12 := -DY / L;
M21 := DY / L;
M22 := DX / L;
// Koordinatentransformation teil 1
tmpv := ball2.SpeedVektor;
Vp1 := fVx * M11 + fVy * -M12;
Vp2 := tmpv.x * M11 + tmpv.y * -M12;
If Vp1 - Vp2 < 0 Then exit; // Bälle gehen bereits auseinander, dann Exit
// Koordinatentransformation teil 2 , aus Optimierungsgründen hinter dem Exit.
Vs1 := fVx * -M21 + fVy * M22;
Vs2 := tmpv.x * -M21 + tmpv.y * M22;
// das Verwurschteln der Massen
MTot := fM + ball2.Mass;
Vp1_ := (fM - ball2.Mass) / MTot * Vp1 + 2 * ball2.Mass / MTot * Vp2;
Vp2_ := (ball2.Mass - fM) / MTot * Vp2 + 2 * fM / MTot * Vp1;
// Rücktransformation
fVx := Vp1_ * M11 + Vs1 * M12;
fVy := Vp1_ * M21 + Vs1 * M22;
tmpv := point(Vp2_ * M11 + Vs2 * M12, Vp2_ * M21 + Vs2 * M22);
ball2.SpeedVektor := tmpv;
End;
End;
Procedure Tball.CalculateMass;
Begin
fm := 4 / 3 * fR * fR * fR * pi;
End;
Procedure Tball.Render(Const Canvas: TCanvas);
Begin
With canvas Do Begin
pen.color := fc;
brush.color := fc;
brush.style := bssolid;
Ellipse(round(fx - fr), round(fy - fr), round(fx + fr), round(fy + fr));
End;
End;
End.