/**
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* @private
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*/
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vec2 cordic(float angle)
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{
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// Scale the vector by the appropriate factor for the 24 iterations to follow.
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vec2 vector = vec2(6.0725293500888267e-1, 0.0);
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// Iteration 1
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float sense = (angle < 0.0) ? -1.0 : 1.0;
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// float factor = sense * 1.0; // 2^-0
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mat2 rotation = mat2(1.0, sense, -sense, 1.0);
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vector = rotation * vector;
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angle -= sense * 7.8539816339744828e-1; // atan(2^-0)
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// Iteration 2
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sense = (angle < 0.0) ? -1.0 : 1.0;
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float factor = sense * 5.0e-1; // 2^-1
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 4.6364760900080609e-1; // atan(2^-1)
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// Iteration 3
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 2.5e-1; // 2^-2
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 2.4497866312686414e-1; // atan(2^-2)
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// Iteration 4
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.25e-1; // 2^-3
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.2435499454676144e-1; // atan(2^-3)
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// Iteration 5
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 6.25e-2; // 2^-4
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 6.2418809995957350e-2; // atan(2^-4)
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// Iteration 6
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 3.125e-2; // 2^-5
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 3.1239833430268277e-2; // atan(2^-5)
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// Iteration 7
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.5625e-2; // 2^-6
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.5623728620476831e-2; // atan(2^-6)
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// Iteration 8
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 7.8125e-3; // 2^-7
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 7.8123410601011111e-3; // atan(2^-7)
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// Iteration 9
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 3.90625e-3; // 2^-8
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 3.9062301319669718e-3; // atan(2^-8)
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// Iteration 10
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.953125e-3; // 2^-9
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.9531225164788188e-3; // atan(2^-9)
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// Iteration 11
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 9.765625e-4; // 2^-10
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 9.7656218955931946e-4; // atan(2^-10)
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// Iteration 12
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 4.8828125e-4; // 2^-11
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 4.8828121119489829e-4; // atan(2^-11)
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// Iteration 13
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 2.44140625e-4; // 2^-12
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 2.4414062014936177e-4; // atan(2^-12)
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// Iteration 14
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.220703125e-4; // 2^-13
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.2207031189367021e-4; // atan(2^-13)
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// Iteration 15
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 6.103515625e-5; // 2^-14
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 6.1035156174208773e-5; // atan(2^-14)
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// Iteration 16
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 3.0517578125e-5; // 2^-15
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 3.0517578115526096e-5; // atan(2^-15)
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// Iteration 17
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.52587890625e-5; // 2^-16
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.5258789061315762e-5; // atan(2^-16)
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// Iteration 18
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 7.62939453125e-6; // 2^-17
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 7.6293945311019700e-6; // atan(2^-17)
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// Iteration 19
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 3.814697265625e-6; // 2^-18
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 3.8146972656064961e-6; // atan(2^-18)
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// Iteration 20
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.9073486328125e-6; // 2^-19
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 1.9073486328101870e-6; // atan(2^-19)
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// Iteration 21
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 9.5367431640625e-7; // 2^-20
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 9.5367431640596084e-7; // atan(2^-20)
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// Iteration 22
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 4.76837158203125e-7; // 2^-21
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 4.7683715820308884e-7; // atan(2^-21)
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// Iteration 23
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 2.384185791015625e-7; // 2^-22
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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angle -= sense * 2.3841857910155797e-7; // atan(2^-22)
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// Iteration 24
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sense = (angle < 0.0) ? -1.0 : 1.0;
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factor = sense * 1.1920928955078125e-7; // 2^-23
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rotation[0][1] = factor;
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rotation[1][0] = -factor;
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vector = rotation * vector;
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// angle -= sense * 1.1920928955078068e-7; // atan(2^-23)
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return vector;
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}
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/**
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* Computes the cosine and sine of the provided angle using the CORDIC algorithm.
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*
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* @name czm_cosineAndSine
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* @glslFunction
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*
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* @param {float} angle The angle in radians.
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*
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* @returns {vec2} The resulting cosine of the angle (as the x coordinate) and sine of the angle (as the y coordinate).
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*
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* @example
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* vec2 v = czm_cosineAndSine(czm_piOverSix);
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* float cosine = v.x;
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* float sine = v.y;
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*/
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vec2 czm_cosineAndSine(float angle)
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{
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if (angle < -czm_piOverTwo || angle > czm_piOverTwo)
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{
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if (angle < 0.0)
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{
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return -cordic(angle + czm_pi);
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}
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else
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{
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return -cordic(angle - czm_pi);
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}
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}
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else
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{
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return cordic(angle);
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}
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}
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