Zoom shader for sphere

Zoom-Shader-Processing.pde

PShader shader;
PImage tex;
PShape sphere;
PVector lensCenter = new PVector(0,0,1);
float zoom = 2;

void setup() {
  size(1169, 1169, P3D);
  tex = loadImage("1539.jpg");
  sphere = createShape(SPHERE, height/2);
  sphere.rotateY(HALF_PI);
  sphere.setTexture(tex);
  sphere.setStroke(false);
}

void draw() {
  ortho();
  background(0);
  translate(width/2, height/2);

  try {
    shader = loadShader("lens.glsl");
    shader.set("lensCenter", lensCenter.x,lensCenter.y,lensCenter.z);
    shader.set("zoom", zoom);
    shader(shader);
    shape(sphere);
    resetShader();
  }
  catch (Exception e) {
    println(e);
  }
}

void mouseWheel(MouseEvent event) {
  zoom += event.getCount() *.01;
  zoom = constrain(zoom, 1, 4);
}

void mouseMoved() {
  lensCenter = toSphere(.5-float(mouseX)/width, -.5+float(mouseY)/height);
}


PVector toSphere(float x, float y) {  //-0.5 ... +0.5
  PVector v = new PVector(x, y);
  if (v.mag()<=1.0f) v.z = sqrt(1.0 - (v.x*v.x) - (v.y*v.y)); //USING (v.x*v.x) - (v.y*v.y) instead of v.mag() !!!
  v.normalize();
  return v;
}

zoom-shader-sphere.glsl

uniform sampler2D texture;
uniform vec3 lensCenter;
uniform float zoom;
varying vec4 vertTexCoord;

float PI = 3.1415;

vec3 toSpherical(vec2 uv) {
  float theta = uv.x * 2.0 * PI - PI/2;
  float phi = (1.0 - uv.y) * PI;
  return vec3(sin(phi) * cos(theta), cos(phi), sin(phi) * sin(theta));
}

vec2 fromSpherical(vec3 p) {
  float theta = atan(p.z, p.x) + PI / 2.0;
  float phi = acos(p.y);
  return vec2(theta / (2.0 * PI), 1.0 - phi / PI);
}

vec3 mixedLens(vec3 lensCenter, vec3 dir, float dist, float lensRadius, float zoom) {
  float mixStart = lensRadius-.05;
  float w = smoothstep(mixStart, lensRadius, dist);
  vec3 linearPart = dir * dist / zoom;
  vec3 quadraticPart = dir * pow(dist / lensRadius, zoom) * lensRadius;
  vec3 sphereCoords = lensCenter + mix(linearPart, quadraticPart, w);
  return sphereCoords;
}

void main() {
  vec3 sphereCoords = toSpherical(vertTexCoord.st);
  float lensRadius = 0.35;
  vec3 dir = sphereCoords - lensCenter;
  float dist = length(dir);

  if (abs(dist-lensRadius)<.005) {
    gl_FragColor = vec4(0.,0.,0.,1.); //yellow border

  } else if (dist < lensRadius) {
    dir = normalize(dir);
    sphereCoords = mixedLens(lensCenter, dir, dist, lensRadius, zoom);
    vec2 uv = fromSpherical(sphereCoords);
    gl_FragColor = texture2D(texture, uv);
  }

  else {
    gl_FragColor = texture2D(texture, vertTexCoord.st); // * vec4(.6,.6,.6,1);
  }

}

Lens-Effect.480.mov