2.51

练习 2.51 定义对画家的 below 操作，它以两个画家为参数。在给定了一个框架后，由 below 得到的画家将要求第一个画家在框架的下部画图，要求第二个画家在框架的上部画图。请按两种方式定义 below：首先写出一个类似于上面 beside 的过程；另一个则直接通过beside和适当的旋转操作（来自练习2.50）完成有关工作。

为了方便直观地体验，将采用 js 实现。

先复用一下上一练习的代码：

 
cons = (x, y) => [x, y];
car = (z) => z[0];
cdr = (z) => z[1];
​
makeVect = cons;
xCorVect = car;
yCorVect = cdr;
​
makeSegment = cons;
startSegment = car;
endSegment = cdr;
​
o = makeVect(0, 0);
e1 = makeVect(300, 0);
e2 = makeVect(0, 150); 
​
s = makeSegment(makeVect(1, 0), makeVect(0, 1)); 
console.log('s = ', s);
​
console.log(startSegment(s));
console.log(endSegment(s));
​x
 
"s = " Array [
  Array [
    1,
    0,
  ],
  Array [
    0,
    1,
  ],
]
Array [
  1,
  0,
]
Array [
  0,
  1,
]
undefined

 
makeFrame = (origin, edge1, edge2) => {
  return [origin, edge1, edge2];
};
​
originFrame = (frame) => frame[0];
edge1Frame = (frame) => frame[1];
edge2Frame = (frame) => frame[2];
​
addVect = (v1, v2) => makeVect(xCorVect(v1) + xCorVect(v2), yCorVect(v1) + yCorVect(v2));
subVect = (v1, v2) => makeVect(xCorVect(v1) - xCorVect(v2), yCorVect(v1) - yCorVect(v2));
scaleVect = (s, v) => makeVect(s * xCorVect(v), s * yCorVect(v));
​
frameCoordMap = (frame) => {
  return (v) => {
    return addVect(
      originFrame(frame),
      addVect(
        scaleVect(
          xCorVect(v),
          edge1Frame(frame)
        ),
        scaleVect(
          yCorVect(v),
          edge2Frame(frame)
        )
      )
    );
  };
}
​
f = makeFrame(o, e1, e2);
 
Array [
  Array [
    0,
    0,
  ],
  Array [
    300,
    0,
  ],
  Array [
    0,
    150,
  ],
]

 
drawLine = (v1, v2) => {
  return (ctx) => {
    ctx.beginPath();
    ctx.moveTo(xCorVect(v1), yCorVect(v1));
    ctx.lineTo(xCorVect(v2), yCorVect(v2));
    ctx.stroke();
  }
};
​
segmentsPainter = (segmentList) => {
  return (frame) => (ctx) => {
    segmentList.forEach((segment) => {
      drawLine(
        (frameCoordMap(frame))(startSegment(segment)),
        (frameCoordMap(frame))(endSegment(segment))
      )(ctx);
    });
  }
}
​
applyToCanvas = (painter, canvasSelector) => {
  const canvas = document.querySelector(canvasSelector);
  const ctx = canvas.getContext('2d');
​
  ctx.clearRect(0, 0, canvas.width, canvas.height); 
​
  painter(ctx);
}
 
[Function applyToCanvas]

 
wavePainter = (frame) => {
  const v1 = makeVect(0.4, 0);
  const v2 = makeVect(0.6, 0);
  const v3 = makeVect(0, 0.2);
  const v4 = makeVect(0.3, 0.2);
  const v5 = makeVect(0.7, 0.2);
  const v6 = makeVect(0, 0.4);
  const v7 = makeVect(0.2, 0.4);
  const v8 = makeVect(0.3, 0.35);
  const v9 = makeVect(0.42, 0.4);
  const v10 = makeVect(0.6, 0.4);
  const v11 = makeVect(0.8, 0.4);
  const v12 = makeVect(0.3, 0.4);
  const v13 = makeVect(0.2, 0.55);
  const v14 = makeVect(0.31, 0.5);
  const v15 = makeVect(0.6, 0.51);
  const v16 = makeVect(1, 0.7);
  const v17 = makeVect(0.5, 0.8);
  const v18 = makeVect(1, 0.85);
  const v19 = makeVect(0.35, 1);
  const v20 = makeVect(0.4, 1);
  const v21 = makeVect(0.6, 1);
  const v22 = makeVect(0.7, 1);
​
  return segmentsPainter([
    makeSegment(v1, v4),
    makeSegment(v2, v5),
    makeSegment(v3, v7), 
    makeSegment(v7, v8),
    makeSegment(v8, v9),
    makeSegment(v9, v4),
    makeSegment(v10, v5),
    makeSegment(v10, v11),
    makeSegment(v6, v13),
    makeSegment(v13, v12),
    makeSegment(v12, v14),
    makeSegment(v16, v11),
    makeSegment(v18, v15),
    makeSegment(v19, v14),
    makeSegment(v20, v17),
    makeSegment(v21, v17),
    makeSegment(v22, v15),
  ])(frame); 
}
 
[Function wavePainter]

 
transformPainter = (painter, origin, corner1, corner2) => {
  return (frame) => {
    const m = frameCoordMap(frame);
    const newOrigin = m(origin);
    return painter(
      makeFrame(
        newOrigin, 
        subVect(m(corner1), newOrigin),
        subVect(m(corner2), newOrigin)
      )
    );
  }
}
​
flipHoriz = (painter) => {
  return transformPainter(
    painter,
    makeVect(1, 0),
    makeVect(0, 0),
    makeVect(1, 1)
  )
}
 
[Function flipHoriz]

 
rotateLeft180 = (painter) => {
  return transformPainter(
    painter,
    makeVect(1, 1),
    makeVect(0, 1),
    makeVect(1, 0)
  )
}
 
[Function rotateLeft180]

 
rotateLeft270 = (painter) => {
  return transformPainter(
    painter,
    makeVect(1, 0),
    makeVect(1, 1),
    makeVect(0, 0)
  )
}
 
[Function rotateLeft270]

第一种方式：

 
const below = (painter1, painter2) => {
  const splitPoint = makeVect(0, 0.5);
  const paintBelow = transformPainter(
    painter1,
    splitPoint,
    makeVect(1, 0.5),
    makeVect(0, 1)
  );
  const paintUp = transformPainter(
    painter2,
    makeVect(0, 0),
    makeVect(1, 0),
    splitPoint
  );
​
  return frame => ctx => {
    paintBelow(frame)(ctx);
    paintUp(frame)(ctx);
  }
}
​
applyToCanvas(below(wavePainter, wavePainter)(f), '#below-1-canvas');
 
undefined

第二种方式

 
const beside = (painter1, painter2) => {
  const splitPoint = makeVect(0.5, 0);
  const paintLeft = transformPainter(
    painter1, 
    makeVect(0, 0),
    splitPoint,
    makeVect(0, 1)
  );
  const paintRight = transformPainter(
    painter2,
    splitPoint,
    makeVect(1, 0),
    makeVect(0.5, 1)
  );
​
  return frame => ctx => {
    paintLeft(frame)(ctx);
    paintRight(frame)(ctx);
  };
};
​
const below = beside;
​
applyToCanvas(
  rotateLeft270(
    below(
      rotateLeft270(rotateLeft270(rotateLeft270(wavePainter))), 
      rotateLeft270(rotateLeft270(rotateLeft270(wavePainter)))
    )
  )(f), 
  '#below-2-canvas');
 
undefined

 
console.log('done');
 
"done"
undefined