java - Orthogonal projection of a point onto a line in processing? -

i have line segment , circle in processing sketch. want center of circle, point q, find closest point, p, on line segment , circle move towards it. i'm not quite sure how code (in processing), suggestions great! thanks! code far:

int xpos1 = 200; int ypos1 = 200; int xp1 = 50; int yp1 = 50; int xp2 = 350; int yp2 = 50;  void setup() {     size(400, 400);      strokeweight(2);     line(xp1, yp1, xp2, yp2);     strokeweight(1); }  void draw() {     drawcircle(); }  void drawcircle() {     fill(50, 120, 120);     //circle     ellipse(xpos1, ypos1, 75, 75);      //circle center     ellipse(xpos1, ypos1, 7, 7);       fill(255);     text("q", xpos1 + 15, ypos1 + 5);     fill(50, 120, 120); } 

the projection of point onto line follows:

start line of form x = + t * n , point p.

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the vector compontent representing nearest point on line point p is:

(a - p) - ((a - p) dot n)n

so have: p + (a - p) - ((a - p) dot n)n

after simplification have: - ((a - p) dot n)n

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note ((a - p) dot n) n vector component represents position along line nearest point beginning (i.e. nearest point p a)

let's use pvectors make life bit easier.

pvector p = new pvector(200, 200); pvector = new pvector(50, 50); pvector b = new pvector(350, 50); pvector n = new pvector(350, 50); // |p2 - p1|  void setup() {     size(400, 400);      strokeweight(2);     strokeweight(1);      // initialize our normalized (unit length) line direction     n.sub(a);     n.normalize(); }  void draw() {     drawcircle(); }  pvector getnearestpointonline(pvector p, pvector a, pvector n){     // notation turns computation inside out,     // equivalent above equation     pvector q = pvector.mult(n, -pvector.sub(a, p).dot(n));     q.add(a);     return q; }  void drawcircle() {     // lets draw here can see     background(255, 255, 255);     line(a.x, a.y, b.x, b.y);      fill(50, 120, 120);     //circle      // note: may require hooking mouse move event handler     p.x = mousex;     p.y = mousey;     pvector q = getnearestpointonline(p, a, n);      ellipse(q.x, q.y, 75, 75);      //circle center     ellipse(q.x, q.y, 7, 7);       fill(0); // make text visible on white background     text("q", q.x + 15, q.y + 5);     //fill(50, 120, 120); } 

reference: https://en.wikipedia.org/wiki/distance_from_a_point_to_a_line#vector_formulation