问题
I'm working with custom drawing / 2D animation and I'm trying to figure out how to detect when the moving object collides with a wall in the map. User holds arrow keys on the keyboard to move the object, and the map is stored as an array structure of points. The walls in the map may be angled, but no curved walls.
Using the map structure (FMap: TMap;) in my code below, in the DoMove property, how do I detect if the object is colliding with any wall in the map and prevent it from moving through? In DoMove, I need to read FMap (refer to DrawMap to see how FMap works) and somehow determine if the object is approaching any wall and stop it.
I could do a dual X/Y loop iterating every possible pixel between each two points in each part of each map, but I already know this will be heavy, considering this procedure will be called rapidly so long as the object is moving.
I thought of reading the pixel colors in the direction the object's moving, and if there's any black (from map lines), consider it a wall. But eventually there will be more custom drawing of a background, so reading pixel colors wouldn't work.
uMain.pas
unit uMain;
interface
uses
Winapi.Windows, Winapi.Messages,
System.SysUtils, System.Variants, System.Classes,
Vcl.Graphics, Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.ExtCtrls;
const
//Window client size
MAP_WIDTH = 500;
MAP_HEIGHT = 500;
type
TKeyStates = Array[0..255] of Bool;
TPoints = Array of TPoint;
TMap = Array of TPoints;
TForm1 = class(TForm)
Tmr: TTimer;
procedure FormKeyDown(Sender: TObject; var Key: Word; Shift: TShiftState);
procedure FormKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState);
procedure TmrTimer(Sender: TObject);
procedure FormCreate(Sender: TObject);
procedure FormDestroy(Sender: TObject);
procedure FormPaint(Sender: TObject);
private
FBMain: TBitmap; //Main rendering image
FBMap: TBitmap; //Map image
FBObj: TBitmap; //Object image
FKeys: TKeyStates; //Keyboard states
FPos: TPoint; //Current object position
FMap: TMap; //Map line structure
procedure Render;
procedure DrawObj;
procedure DoMove;
procedure DrawMap;
procedure LoadMap;
public
end;
var
Form1: TForm1;
implementation
{$R *.dfm}
uses
Math, StrUtils;
procedure TForm1.FormCreate(Sender: TObject);
begin
FBMain:= TBitmap.Create;
FBMap:= TBitmap.Create;
FBObj:= TBitmap.Create;
ClientWidth:= MAP_WIDTH;
ClientHeight:= MAP_HEIGHT;
FBMain.Width:= MAP_WIDTH;
FBMain.Height:= MAP_HEIGHT;
FBMap.Width:= MAP_WIDTH;
FBMap.Height:= MAP_HEIGHT;
FBObj.Width:= MAP_WIDTH;
FBObj.Height:= MAP_HEIGHT;
FBObj.TransparentColor:= clWhite;
FBObj.Transparent:= True;
FPos:= Point(150, 150);
LoadMap; //Load map lines into array structure
DrawMap; //Draw map lines to map image only once
Tmr.Enabled:= True;
end;
procedure TForm1.FormDestroy(Sender: TObject);
begin
Tmr.Enabled:= False;
FBMain.Free;
FBMap.Free;
FBObj.Free;
end;
procedure TForm1.LoadMap;
begin
SetLength(FMap, 1); //Just one object on map
//Triangle
SetLength(FMap[0], 4); //4 points total
FMap[0][0]:= Point(250, 100);
FMap[0][1]:= Point(250, 400);
FMap[0][2]:= Point(100, 400);
FMap[0][3]:= Point(250, 100);
end;
procedure TForm1.FormKeyDown(Sender: TObject; var Key: Word;
Shift: TShiftState);
begin
FKeys[Key]:= True;
end;
procedure TForm1.FormKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState);
begin
FKeys[Key]:= False;
end;
procedure TForm1.FormPaint(Sender: TObject);
begin
Canvas.Draw(0, 0, FBMain); //Just draw rendered image to form
end;
procedure TForm1.DoMove;
const
SPD = 3; //Speed (pixels per movement)
var
X, Y: Integer;
P: TPoints;
begin
//How to keep object from passing through map walls?
if FKeys[VK_LEFT] then begin
//Check if there's a wall on the left
FPos.X:= FPos.X - SPD;
end;
if FKeys[VK_RIGHT] then begin
//Check if there's a wall on the right
FPos.X:= FPos.X + SPD;
end;
if FKeys[VK_UP] then begin
//Check if there's a wall on the top
FPos.Y:= FPos.Y - SPD;
end;
if FKeys[VK_DOWN] then begin
//Check if there's a wall on the bottom
FPos.Y:= FPos.Y + SPD;
end;
end;
procedure TForm1.DrawMap;
var
C: TCanvas;
X, Y: Integer;
P: TPoints;
begin
C:= FBMap.Canvas;
//Clear image first
C.Brush.Style:= bsSolid;
C.Pen.Style:= psClear;
C.Brush.Color:= clWhite;
C.FillRect(C.ClipRect);
//Draw map walls
C.Brush.Style:= bsClear;
C.Pen.Style:= psSolid;
C.Pen.Width:= 2;
C.Pen.Color:= clBlack;
for X := 0 to Length(FMap) - 1 do begin
P:= FMap[X]; //One single map object
for Y := 0 to Length(P) - 1 do begin
if Y = 0 then //First iteration only
C.MoveTo(P[Y].X, P[Y].Y)
else //All remaining iterations
C.LineTo(P[Y].X, P[Y].Y);
end;
end;
end;
procedure TForm1.DrawObj;
var
C: TCanvas;
R: TRect;
begin
C:= FBObj.Canvas;
//Clear image first
C.Brush.Style:= bsSolid;
C.Pen.Style:= psClear;
C.Brush.Color:= clWhite;
C.FillRect(C.ClipRect);
//Draw object in current position
C.Brush.Style:= bsClear;
C.Pen.Style:= psSolid;
C.Pen.Width:= 2;
C.Pen.Color:= clRed;
R.Left:= FPos.X - 10;
R.Right:= FPos.X + 10;
R.Top:= FPos.Y - 10;
R.Bottom:= FPos.Y + 10;
C.Ellipse(R);
end;
procedure TForm1.Render;
begin
//Combine map and object images into main image
FBMain.Canvas.Draw(0, 0, FBMap);
FBMain.Canvas.Draw(0, 0, FBObj);
Invalidate; //Repaint
end;
procedure TForm1.TmrTimer(Sender: TObject);
begin
DoMove; //Control movement of object
DrawObj; //Draw object
Render;
end;
end.
uMain.dfm
object Form1: TForm1
Left = 315
Top = 113
BorderIcons = [biSystemMenu]
BorderStyle = bsSingle
Caption = 'Form1'
ClientHeight = 104
ClientWidth = 207
Color = clBtnFace
DoubleBuffered = True
Font.Charset = DEFAULT_CHARSET
Font.Color = clWindowText
Font.Height = -11
Font.Name = 'Tahoma'
Font.Style = []
OldCreateOrder = False
Position = poScreenCenter
OnCreate = FormCreate
OnDestroy = FormDestroy
OnKeyDown = FormKeyDown
OnKeyUp = FormKeyUp
OnPaint = FormPaint
PixelsPerInch = 96
TextHeight = 13
object Tmr: TTimer
Enabled = False
Interval = 50
OnTimer = TmrTimer
Left = 24
Top = 8
end
end
PS - This code is just a stripped and dummied version of my full project to demonstrate how things work.
EDIT
I just realized an important factor: Right now, I've only implemented one moving object. However, there will be multiple moving objects as well. So, the collision may occur with either a map wall or another object (which I'll have each object in a list). The full project is still very raw like this sample, but much more code than is relevant for this question.
回答1:
this unit found on the web (can't remember where, no author mentioned, perhaps someone can provide a link) would give you the ability of calculating collisions and reflection angles.
unit Vector;
interface
type
TPoint = record
X, Y: Double;
end;
TVector = record
X, Y: Double;
end;
TLine = record
P1, P2: TPoint;
end;
function Dist(P1, P2: TPoint): Double; overload;
function ScalarProd(P1, P2: TVector): Double;
function ScalarMult(P: TVector; V: Double): TVector;
function Subtract(V1, V2: TVector): TVector; overload;
function Subtract(V1, V2: TPoint): TVector; overload;
function MinDistPoint(Point: TPoint; Line: TLine): TPoint;
function Mirror(W, V: TVector): TVector;
function Dist(Point: TPoint; Line: TLine): Double; overload;
implementation
function Dist(P1, P2: TPoint): Double; overload;
begin
Result := Sqrt(Sqr(P1.X - P2.X) + Sqr(P1.Y - P2.Y));
end;
function ScalarProd(P1, P2: TVector): Double;
begin
Result := P1.X * P2.X + P1.Y * P2.Y;
end;
function ScalarMult(P: TVector; V: Double): TVector;
begin
Result.X := P.X * V;
Result.Y := P.Y * V;
end;
function Subtract(V1, V2: TVector): TVector; overload;
begin
Result.X := V2.X - V1.X;
Result.Y := V2.Y - V1.Y;
end;
function Subtract(V1, V2: TPoint): TVector; overload;
begin
Result.X := V2.X - V1.X;
Result.Y := V2.Y - V1.Y;
end;
function MinDistPoint(Point: TPoint; Line: TLine): TPoint;
var
U: Double;
P: TPoint;
begin
U := ((Point.X - Line.P1.X) * (Line.P2.X - Line.P1.X) +
(Point.Y - Line.P1.Y) * (Line.P2.Y - Line.P1.Y)) /
(Sqr(Line.P1.X - Line.P2.X) + Sqr(Line.P1.Y - Line.P2.Y));
if U <= 0 then
Exit(Line.P1);
if U >= 1 then
Exit(Line.P2);
P.X := Line.P1.X + U * (Line.P2.X - Line.P1.X);
P.Y := Line.P1.Y + U * (Line.P2.Y - Line.P1.Y);
Exit(P);
end;
function Mirror(W, V: TVector): TVector;
begin
Result := Subtract(ScalarMult(V, 2*ScalarProd(v,w)/ScalarProd(v,v)), W);
end;
function Dist(Point: TPoint; Line: TLine): Double; overload;
begin
Result := Dist(Point, MinDistPoint(Point, Line));
end;
end.
An example implementation would be
unit BSP;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, StdCtrls, Vector, ExtCtrls;
type
TForm2 = class(TForm)
Timer1: TTimer;
procedure FormPaint(Sender: TObject);
procedure FormCreate(Sender: TObject);
procedure Timer1Timer(Sender: TObject);
private
{ Private-Deklarationen }
FLines: array of TLine;
FP: TPoint;
FV: TVector;
FBallRadius: Integer;
FBallTopLeft: Windows.TPoint;
public
{ Public-Deklarationen }
end;
var
Form2: TForm2;
implementation
{$R *.dfm}
procedure TForm2.FormCreate(Sender: TObject);
const
N = 5;
var
I: Integer;
begin
Randomize;
SetLength(FLines, 4 + N);
FBallRadius := 15;
// Walls
FLines[0].P1.X := 0;
FLines[0].P1.Y := 0;
FLines[0].P2.X := Width - 1;
FLines[0].P2.Y := 0;
FLines[1].P1.X := Width - 1;
FLines[1].P1.Y := 0;
FLines[1].P2.X := Width - 1;
FLines[1].P2.Y := Height - 1;
FLines[2].P1.X := Width - 1;
FLines[2].P1.Y := Height - 1;
FLines[2].P2.X := 0;
FLines[2].P2.Y := Height - 1;
FLines[3].P1.X := 0;
FLines[3].P1.Y := 0;
FLines[3].P2.X := 0;
FLines[3].P2.Y := Height - 1;
for I := 0 to N - 1 do
begin
FLines[I + 4].P1.X := 50 + Random(Width - 100);
FLines[I + 4].P1.Y := 50 + Random(Height - 100);
FLines[(I + 1) mod N + 4].P2 := FLines[I + 4].P1;
end;
FP.X := 50;
FP.Y := 50;
FV.X := 10;
FV.Y := 10;
end;
procedure TForm2.FormPaint(Sender: TObject);
const
Iterations = 100;
var
I, MinIndex, J: Integer;
MinDist, DP, DH: Double;
MP: TPoint;
H: TPoint;
begin
for I := 0 to Length(FLines) - 1 do
begin
Canvas.MoveTo(Round(FLines[I].P1.X), Round(FLines[I].P1.Y));
Canvas.LineTo(Round(FLines[I].P2.X), Round(FLines[I].P2.Y));
end;
for I := 0 to Iterations do
begin
H := FP;
FP.X := FP.X + FV.X / Iterations;
FP.Y := FP.Y + FV.Y / Iterations;
MinDist := Infinite;
MinIndex := -1;
for J := 0 to Length(FLines) - 1 do
begin
DP := Dist(FP, FLines[J]);
DH := Dist(H, FLines[J]);
if (DP < MinDist) and (DP < DH) then
begin
MinDist := DP;
MinIndex := J;
end;
end;
if MinIndex >= 0 then
if Sqr(MinDist) < 2*Sqr(FBallRadius * 0.7 / 2)
then
begin
MP := MinDistPoint(FP, FLines[MinIndex]);
FV := Mirror(FV, Subtract(MP, FP));
end;
end;
FBallTopLeft.X := Round(FP.X - FBallRadius);
FBallTopLeft.Y := Round(FP.Y - FBallRadius);
Canvas.Brush.Color := clBlue;
Canvas.Ellipse(FBallTopLeft.X, FBallTopLeft.Y,
FBallTopLeft.X + FBallRadius * 2, FBallTopLeft.Y + FBallRadius * 2);
end;
procedure TForm2.Timer1Timer(Sender: TObject);
begin
invalidate;
end;
end.
回答2:
Every time the key is pressed, you compute the new coordinate of the object after the move would be executed. Then you can test for intersections between the object trajectory and the line in the map.
Since your map can be considered a set of line segments, and given that your object path is linear, you can find all the possible collisions by finding intersections between the object path and the lines on which the segments of your map lie. You will only have two slopes for the object path: zero and infinity. So for each map segment:
- Compute its slope. If the map segment slope is the same as object path slope, they will not intersect.
- Compute the intersection between the lines that the map segment and the object path are one (see here for instance)
- Check if the map segment ends before the collision point: if yes, then no collision
- Check if the object path ends before the collision point: if yes, then no collision
回答3:
If not doing it yourself is OK, you could use ready made library for this task. Box2D has Delphi version here
回答4:
I had already half-way answered my own question in the question its self. One thing I had thought of was reading the pixels of the image in the direction of the movement, and check if there's a line there or not. I now realize that I can have an extra layer under the FBMap map layer for the background, and leave the map layer as it is with only the collidable walls drawn.
When moving, scan the pixels in the direction of the movement on that particular layer, not the full image. Since I already have a pre-drawn layer sitting there, I can read it rather than the main image. Based on the speed of movement, I only need to look so many pixels ahead (at least a few more pixels than the number of pixels of movement).
Also, in case the background of the image has a picture representing the walls rather than straight plain lines, then this layer doesn't even have to be drawn at all. This layer can be explicitly used just for scanning a few pixels ahead of movement for collision areas. As a matter of fact, since I also need to recognize collision with other moving objects, I can draw all the objects on here as well (in black/white).
A few iterations of pixels across a canvas, for example 20, is nothing compared to extensive iterations through the map lines, for example 2000.
来源：https://stackoverflow.com/questions/15308077/delphi-custom-animation-collision-detection