detectcollision - 判断粒子是否与固壁碰撞（碰撞检测）

% detectcollision.m

% detect the collision between a particle and obstructions

% particle moves from (x1,y1) to (x2,y2) in a line

% particle is represented with a point (radius=0)

% obstructions are defined in matrix 'elems', element=0: obstruction, element=1: void space

% output: ifcollide, 0: no collision, 1: collision

function ifcollide = detectcollision(x1,y1,x2,y2,elems)

ifcollide=0;

% upper boundary

[uby ubx]=size(elems);

uby=uby-1;

ubx=ubx-1;

if x2<0 || x2>ubx || y2<0 || y2>uby

    ifcollide=1;

    return

end

% y limits

maxy=floor(max(y2,y1));

miny=floor(min(y2,y1));

% moving direction in x

sgndx=sign(x1-x2);

if sgndx~=0

    % equation of the trajectory: y=ax+c

    a=(y2-y1)/(x2-x1);

    c=-a*x1+y1;

    if a>0

        for xtrack=floor(x2):sgndx:floor(x1)      % all integer x coodinates on the track

            for ytrack=max(miny,ceil(xtrack*a+c-1)):min(maxy,floor((xtrack+1)*a+c))  % all integer y coordinates of elements penetrated by the line

                if elems(ytrack+1,xtrack+1)==0

                    ifcollide=1;

                    return

                end

            end

        end

    else

        for xtrack=floor(x2):sgndx:floor(x1)

            for ytrack=max(miny,ceil((xtrack+1)*a+c-1)):min(maxy,floor(xtrack*a+c))

                if elems(ytrack+1,xtrack+1)==0

                    ifcollide=1;

                    return

                end 

            end

        end

    end

else

    sgndy=sign(y1-y2);

    if sgndy~=0

        for ytrack=floor(y2):sgndy:floor(y1)

             if elems(ytrack+1,floor(x1)+1)==0

                ifcollide=1;

                return

            end

        end

    end

end