与圆相切

Question

I'm writing curve snake game like this http://www.gamekb.com/thumbs_v2/01872/1872657-85play-curve-fever-2.gif in Java. If I want to move under specific angle it:

posX += cos(angle);
posY += sin(angle);

When I press Left or Right it calculates middles of rotating (for left and for right) and then

posX = middleX + sin(angle) * radius;
posY = middleY + cos(angle) * radius;

angle += PI/180;

And if I release the key it should calculate new angle:

vectorx = middleX - posX; /*normal vector to tangent*/
vectory = middleY - posY;

k = -(vectorx/vectory);   /*directiv of tangent. Should be angle in radians but not
                           in all cases */

angle = k;

This piece of code means I calculate vector[vectorx, vectory] that is perpendicular to my new straight with angle I am calculating and k is from parametric form of straight and it is angle in radians, basically I'm trying to make a tangent to the circle in point where I release the arrow.

Answer 1

You haven't specified what angle represents when the snake is turning. It could be trivial to calculate the new angle just using old one, but here is a way using the tangent:

vectorX = posX - middleX;
vectorY = posY - middleY;
tangentX = -vectorY; // flip the signs of these two for
tangentY = +vectorX; // turning in the other direction
angle = atan2(tangentY, tangentX)

An alternative way is to keep the meaning of angle as the snake's direction and forget about the centre of the circle and the tangent. When the snake turns, 1 / radius is added or subtracted from angle and the position is still calculated using posX += cos(angle), posY += sin(angle) .