Canvas.setpenopacity(0.25);

const turtle = new Turtle();

const slices = 40
const stacks = 20
let quadWidth = 0.04
let quadHeight = 0.02

let camera = new Camera([1, 3, -5], [0, 0, 0]);

function walk(i) {
    let v = (i % slices) / slices
    let u = Math.floor(i / slices) / stacks
    
    renderPoint(u, v, mobiusTube)

    return i < stacks * slices;
}

function mobiusTube(u, v) {
    u = Math.PI * u
    v = 2 * Math.PI * v
    
    R = 1.5
    n = 3
    u = u * 2
    x = (1.0*R + 0.125*Math.sin(u/2)*Math.pow(Math.abs(Math.sin(v)), 2/n)*Math.sign(Math.sin(v)) + 0.5*Math.cos(u/2)*Math.pow(Math.abs(Math.cos(v)), 2/n)*Math.sign(Math.cos(v)))*Math.cos(u)
    y = (1.0*R + 0.125*Math.sin(u/2)*Math.pow(Math.abs(Math.sin(v)), 2/n)*Math.sign(Math.sin(v)) + 0.5*Math.cos(u/2)*Math.pow(Math.abs(Math.cos(v)), 2/n)*Math.sign(Math.cos(v)))*Math.sin(u)
    z = -0.5*Math.sin(u/2)*Math.pow(Math.abs(Math.cos(v)), 2/n)*Math.sign(Math.cos(v)) + 0.125*Math.cos(u/2)*Math.pow(Math.abs(Math.sin(v)), 2/n)*Math.sign(Math.sin(v))
    return [x, y, z]
}

function kleinBottle(u, v) {
    u = Math.PI * u
    v = 2 * Math.PI * v

    u = u * 2
    if (u < Math.PI) {
        x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(u) * Math.cos(v)
        z = -8 * Math.sin(u) - 2 * (1 - Math.cos(u) / 2) * Math.sin(u) * Math.cos(v)
    }
    else {
        x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(v + Math.PI)
        z = -8 * Math.sin(u)
    }
    y = -2 * (1 - Math.cos(u) / 2) * Math.sin(v)
    return [x * 0.25, y * 0.25, z * 0.25]
}

function renderPoint(u, v, paramFunc) {
    let quad = []
    quad[0] = paramFunc(u + quadWidth, v + quadHeight)
    quad[1] = paramFunc(u + quadWidth * 2, v + quadHeight)
    quad[2] = paramFunc(u + quadWidth * 2, v + quadHeight * 2)
    quad[3] = paramFunc(u + quadWidth, v + quadHeight * 2)

    let visible = isFrontfacing(camera.position, [quad[0], quad[1], quad[2]])

    if (visible) {
        for (let i = 0; i < 4; i++) {
            renderQuad(quad, camera)
        }
    }
    else {
        renderQuad(quad, camera)
    }
}

function renderQuad(quad, camera) {
    turtle.penup()
    turtle.goto(toScreen(quad[3], camera))
    turtle.pendown()
    turtle.goto(toScreen(quad[0], camera))
    turtle.goto(toScreen(quad[1], camera))
    turtle.goto(toScreen(quad[2], camera))
    turtle.goto(toScreen(quad[3], camera))    
}

// 3D rendering

var finalMatrix;
function toScreen(vertex, camera, modelMatrix = []) {
    if (typeof finalMatrix === "undefined") finalMatrix = mat4.create()
    if (modelMatrix.length > 0) {
        mat4.multiply(finalMatrix, camera.getCameraMatrix(), modelMatrix)
        mat4.multiply(finalMatrix, camera.getPerspectiveMatrix(), finalMatrix)
    }
    else {
        mat4.multiply(finalMatrix, camera.getPerspectiveMatrix(), camera.getCameraMatrix())
    }
    
    vertex = vertex.concat(1)
    vec4.transformMat4(vertex, vertex, finalMatrix)
    
    x = vertex[0] / vertex[3]
    y = vertex[1] / vertex[3]
    z = vertex[2] / vertex[3]
    
    // to canvas coords
    x = -x * 50
    y = -y * 50    
    
    return [x, y, z]
}

// Camera

function Camera(position, lookAt) {
    this.position = position
    this.lookAt = lookAt
    this.fov = 0.5
    this.nearPlane = 1
    this.farPlane = 1000
    this.aspect = 1
    
    this.projectionMatrix = []
    this.cameraMatrix = []
    this.dirty = true
    
    this.getPerspectiveMatrix = function() {
        this.updateMatrices()
        return this.projectionMatrix
    }
    
    this.getCameraMatrix = function() {
        this.updateMatrices()
        return this.cameraMatrix
    }
    
    this.updateMatrices = function() {
        if (this.dirty) {
            this.projectionMatrix = mat4.create()
            mat4.perspective(this.projectionMatrix, this.fov, this.aspect, this.nearPlane, this.farPlane)

            this.cameraMatrix = mat4.create()
            mat4.lookAt(this.cameraMatrix, camera.position, camera.lookAt, [0,1,0])
            
            this.dirty = false
        }
    }
}

function isFrontfacing (camPos, triangle) {
    let normal = getNormal(triangle)
    let center = getCenter(triangle)

    let camToTriangle = vec3.subtract([], center, camPos)
    return vec3.dot(camToTriangle, normal) < 0
}

function frontFacingAmount(camPos, triangle) {
    vec3.normalize([], camPos)

    let trianglePos = getCenter(triangle)
    vec3.normalize(trianglePos, trianglePos)
    
    return Math.abs(Math.acos(vec3.dot(trianglePos, localCamera)) / (0.5 * Math.PI))
}

function getSpecular (camPos, lightPos, triangle) {
    // all in local space
    let localCamera = vec3.transformMat4([], camPos, this.invModelMatrix)
    let localLight = vec3.transformMat4([], lightPos, this.invModelMatrix)
    
    let trianglePos = getCenter(triangle)
    let normal = trianglePos
    let viewDirection = vec3.normalize([], vec3.subtract([], localCamera, trianglePos))
    let lightDirection = vec3.normalize([], localLight)
    
    if (vec3.dot(normal, lightDirection) < 0.0) {
        return 0        
    }
    else {
        let inverted = vec3.scale([], lightDirection, -1)
        let reflected = this.reflect(inverted, normal)
        
        let reflectedDotted = vec3.dot(reflected, viewDirection)

        return Math.pow(Math.max(0.0, reflectedDotted), 1)
    }
}

function getCenter(triangle) {
    return [
        (triangle[0][0] + triangle[1][0] + triangle[2][0]) / 3,
        (triangle[0][1] + triangle[1][1] + triangle[2][1]) / 3,
        (triangle[0][2] + triangle[1][2] + triangle[2][2]) / 3,
        ]
}

function getNormal(triangle) {
    let edge1 = vec3.subtract([], triangle[0], triangle[1])
    let edge2 = vec3.subtract([], triangle[1], triangle[2])
    let normal = []
    
    normal[0] = (edge1[1] * edge2[2]) - (edge1[2] * edge2[1])
    normal[1] = (edge1[2] * edge2[0]) - (edge1[0] * edge2[2])
    normal[2] = (edge1[0] * edge2[1]) - (edge1[1] * edge2[0])
    
    vec3.normalize(normal, normal)
    return normal;
}

// gl-matrix

EPSILON = 0.00001;
halfToRad = 0.5 * Math.PI / 180.0;
function vec3() {
    this.add = function(out, a, b) {
      out[0] = a[0] + b[0];
      out[1] = a[1] + b[1];
      out[2] = a[2] + b[2];
      return out;
    }
    this.subtract = function(out, a, b) {
      out[0] = a[0] - b[0];
      out[1] = a[1] - b[1];
      out[2] = a[2] - b[2];
      return out;
    }    
    this.multiply = function(out, a, b) {
      out[0] = a[0] * b[0];
      out[1] = a[1] * b[1];
      out[2] = a[2] * b[2];
      return out;
    }
    this.normalize = function(out, a) {
      let x = a[0];
      let y = a[1];
      let z = a[2];
      let len = x*x + y*y + z*z;
      if (len > 0) {
        //TODO: evaluate use of glm_invsqrt here?
        len = 1 / Math.sqrt(len);
      }
      out[0] = a[0] * len;
      out[1] = a[1] * len;
      out[2] = a[2] * len;
      return out;
    }    
    this.scale = function(out, a, b) {
      out[0] = a[0] * b;
      out[1] = a[1] * b;
      out[2] = a[2] * b;
      return out;
    }
    this.distance = function(a, b) {
        let x = b[0] - a[0];
        let y = b[1] - a[1];
        let z = b[2] - a[2];
        return Math.sqrt(x*x + y*y + z*z);
    }
    this.dot = function (a, b) {
        return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
    }
    this.transformMat4 = function(out, a, m) {
      let x = a[0], y = a[1], z = a[2];
      let w = m[3] * x + m[7] * y + m[11] * z + m[15];
      w = w || 1.0;
      out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
      out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
      out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
      return out;
    }
}
function vec4() {
    this.transformMat4 = function(out, a, m) {
      let x = a[0], y = a[1], z = a[2], w = a[3];
      out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
      out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
      out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
      out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
      return out;
    }
}
function mat4() {
    this.create = function() {
        return new Float32Array(16)
    }
    
    this.identity = function(out) {
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = 1;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 1;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }    
    
    this.lookAt = function(out, eye, center, up) {
      let x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
      let eyex = eye[0];
      let eyey = eye[1];
      let eyez = eye[2];
      let upx = up[0];
      let upy = up[1];
      let upz = up[2];
      let centerx = center[0];
      let centery = center[1];
      let centerz = center[2];
      if (Math.abs(eyex - centerx) < EPSILON &&
          Math.abs(eyey - centery) < EPSILON &&
          Math.abs(eyez - centerz) < EPSILON) {
        return identity(out);
      }
      z0 = eyex - centerx;
      z1 = eyey - centery;
      z2 = eyez - centerz;
      len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
      z0 *= len;
      z1 *= len;
      z2 *= len;
      x0 = upy * z2 - upz * z1;
      x1 = upz * z0 - upx * z2;
      x2 = upx * z1 - upy * z0;
      len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
      if (!len) {
        x0 = 0;
        x1 = 0;
        x2 = 0;
      } else {
        len = 1 / len;
        x0 *= len;
        x1 *= len;
        x2 *= len;
      }
      y0 = z1 * x2 - z2 * x1;
      y1 = z2 * x0 - z0 * x2;
      y2 = z0 * x1 - z1 * x0;
      len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
      if (!len) {
        y0 = 0;
        y1 = 0;
        y2 = 0;
      } else {
        len = 1 / len;
        y0 *= len;
        y1 *= len;
        y2 *= len;
      }
      out[0] = x0;
      out[1] = y0;
      out[2] = z0;
      out[3] = 0;
      out[4] = x1;
      out[5] = y1;
      out[6] = z1;
      out[7] = 0;
      out[8] = x2;
      out[9] = y2;
      out[10] = z2;
      out[11] = 0;
      out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
      out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
      out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
      out[15] = 1;
      return out;
    }

    this.multiply = function(out, a, b) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
      // Cache only the current line of the second matrix
      let b0  = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
      out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
      b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
      out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
      b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
      out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
      b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
      out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
      return out;
    }
    
    this.perspective = function(out, fovy, aspect, near, far) {
      let f = 1.0 / Math.tan(fovy / 2), nf;
      out[0] = f / aspect;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = f;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[11] = -1;
      out[12] = 0;
      out[13] = 0;
      out[15] = 0;
      if (far != null && far !== Infinity) {
        nf = 1 / (near - far);
        out[10] = (far + near) * nf;
        out[14] = (2 * far * near) * nf;
      } else {
        out[10] = -1;
        out[14] = -2 * near;
      }
      return out;
    }
        
    this.fromRotationTranslationScale = function(out, q, v, s) {
      // Quaternion math
      let x = q[0], y = q[1], z = q[2], w = q[3];
      let x2 = x + x;
      let y2 = y + y;
      let z2 = z + z;
      let xx = x * x2;
      let xy = x * y2;
      let xz = x * z2;
      let yy = y * y2;
      let yz = y * z2;
      let zz = z * z2;
      let wx = w * x2;
      let wy = w * y2;
      let wz = w * z2;
      let sx = s[0];
      let sy = s[1];
      let sz = s[2];
      out[0] = (1 - (yy + zz)) * sx;
      out[1] = (xy + wz) * sx;
      out[2] = (xz - wy) * sx;
      out[3] = 0;
      out[4] = (xy - wz) * sy;
      out[5] = (1 - (xx + zz)) * sy;
      out[6] = (yz + wx) * sy;
      out[7] = 0;
      out[8] = (xz + wy) * sz;
      out[9] = (yz - wx) * sz;
      out[10] = (1 - (xx + yy)) * sz;
      out[11] = 0;
      out[12] = v[0];
      out[13] = v[1];
      out[14] = v[2];
      out[15] = 1;
      return out;
    }
    
    this.invert = function(out, a) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
      let b00 = a00 * a11 - a01 * a10;
      let b01 = a00 * a12 - a02 * a10;
      let b02 = a00 * a13 - a03 * a10;
      let b03 = a01 * a12 - a02 * a11;
      let b04 = a01 * a13 - a03 * a11;
      let b05 = a02 * a13 - a03 * a12;
      let b06 = a20 * a31 - a21 * a30;
      let b07 = a20 * a32 - a22 * a30;
      let b08 = a20 * a33 - a23 * a30;
      let b09 = a21 * a32 - a22 * a31;
      let b10 = a21 * a33 - a23 * a31;
      let b11 = a22 * a33 - a23 * a32;
      // Calculate the determinant
      let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
      if (!det) {
        return null;
      }
      det = 1.0 / det;
      out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
      out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
      out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
      out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
      out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
      out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
      out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
      out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
      out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
      out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
      out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
      out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
      out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
      out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
      out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
      out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
      return out;
    }    
}
function quat() {
    this.create = function() {
      let out = [];
        out[0] = 0;
        out[1] = 0;
        out[2] = 0;
        out[3] = 1;
        return out;
    }
    this.fromEuler = function(out, x, y, z) {
        x *= halfToRad;
        y *= halfToRad;
        z *= halfToRad;
        let sx = Math.sin(x);
        let cx = Math.cos(x);
        let sy = Math.sin(y);
        let cy = Math.cos(y);
        let sz = Math.sin(z);
        let cz = Math.cos(z);
        out[0] = sx * cy * cz - cx * sy * sz;
        out[1] = cx * sy * cz + sx * cy * sz;
        out[2] = cx * cy * sz - sx * sy * cz;
        out[3] = cx * cy * cz + sx * sy * sz;
        return out;
    }
}
vec3 = new vec3() // mimic static functions behavior
vec4 = new vec4()
quat = new quat()
mat4 = new mat4()
// end gl-matrix