math - tensorflow.js 使用 webgl 绘制心脏

Question

尝试使用公式 here 显示一颗心

 (x²+y²−r²)³−rx²y³=0 

心的内部应遵循以下公式:

(x²+y²−r²)³−rx²y³<0  

但是目前只显示了一半的心

class Heart {
    variableNames = ["X"];
    outputShape;
    userCode;

    constructor(shape) {
        this.outputShape = shape;
        const [h, w] = shape;
        this.userCode = `
      void main() {
        ivec3 coords = getOutputCoords();
        

        float x = float(-coords[0] + ${h} / 2);
        float y = float(-coords[1] + ${w} / 2);
        float a = 100.0;

        float x2 = x * x ;
        float y2 = y * y ;

        float x3 = x2 * x;
        float y3 = y2 * y;
        

        // float val = pow(x2 + y2 - 8120.0, 3.0);
        // float val = (x2 + 9.0*y2/4.0 - 1000.0, 3.0) * (x2 + 9.0*y2/4.0 - 1000.0, 3.0) * (x2 + 9.0*y2/4.0 - 1000.0, 3.0);
        float val = pow(x2 + y2 - a*a, 3.0) - x3*y2*a;
        // float val = x2 + y2 - 1000000.0;

        int r = coords[0];
        int c = coords[1];
        int d = coords[2];

        if(val < 0.0) {
            setOutput(255.0);
            // setOutput(float((getX(r, c, 0) + getX(r, c, 1) + getX(r, c, 2)) / 3.0));
            // if(coords[2] == 0) {
            //     setOutput(float((getX(r, c, d) + getX(r, c, d + 1) + getX(r, c, d + 2)) / 3.0));
            // } else if(coords[2] == 1) {
            //     setOutput(float((getX(r, c, d - 1) + getX(r, c, d) + getX(r, c, d + 1)) / 3.0));
            // } else {
            //     setOutput(float((getX(r, c, d) + getX(r, c, d - 1) + getX(r, c, d - 2)) / 3.0));
            // }
        } else {

            setOutput(getX(r, c, d));
        }

      }
    `;
    }
}


const tensor = tf.ones([400, 300, 3]).cast('int32');
    console.log(tensor.shape);
    /////////////////
    const prog = new Heart(tensor.shape);
    const drawn = tf.backend().compileAndRun(prog, [tensor])
    console.log(drawn);
    const canvas1 = document.createElement('canvas');
    // canvas1.width = 400;
    tf.browser.toPixels(drawn, canvas1);
    console.log(canvas1.width);
    canvas1.width = 800;
    document.body.append(canvas1);

<script src="https://cdn.jsdelivr.net/npm/@tensorflow/tfjs@2.0.0/dist/tf.min.js"></script>

Answer 1

使用 pow(x, y)，根据 doc，当 x<0 或 x=0 且 y≤0 时存在未定义的行为.

要解决它，应该使用显式乘法:

float val = (x*x + y*y - a*a) * (x*x + y*y - a*a) * (x*x + y*y - a*a) - x*x*x*y*y*a;