【发布时间】：2023-03-17 22:36:02
【问题描述】：
是否有可能，如果可以，如何绘制四个角扭曲为非矩形形状的图像。例如，如果您想要绘制图像，就好像它已在 3d 空间中旋转一样。
【问题讨论】：
【发布时间】：2023-03-17 22:36:02
【问题描述】：
我根据 Thatcher Ulrich 的代码 (http://tulrich.com/geekstuff/canvas/perspective.html) 创建了一个简单的 4 点变换。此版本仅提取一小部分三角码并处理几何细分以进行适当的转换。尽情享受吧！
http://jsfiddle.net/mrbendel/6rbtde5t/1/
var controls = [];
var canvas;
var context;
var image;
var triangles = [];
var dirtyTriangles = true;
var rand = function(s,e) {
return Math.random() * (e-s) + s;
}
// dom ready
$(document).ready(function() {
image = new Image();
$(image).load(function() {
setInterval(draw, 1000 / 60);
});
$(image).attr('src', 'http://media.giphy.com/media/NWb6sWXQQTqwg/giphy.gif');
canvas = document.createElement('canvas');
$(canvas).attr('width', 500);
$(canvas).attr('height', 500);
$('body').append(canvas);
context = canvas.getContext('2d');
//
for (var i = 0; i < 4; ++i) {
var control = document.createElement('div');
$(control).addClass('node');
$('body').append(control);
controls.push(control);
}
$(controls[0]).css('left', rand(25, 225));
$(controls[0]).css('top', rand(25, 225));
$(controls[1]).css('left', rand(250, 475));
$(controls[1]).css('top', rand(25, 225));
$(controls[2]).css('left', rand(250, 475));
$(controls[2]).css('top', rand(250, 475));
$(controls[3]).css('left', rand(25, 225));
$(controls[3]).css('top', rand(250, 475));
$('body').mousedown(function(e) {
if ($(e.target).hasClass('node')) {
var node = e.target;
$('body').mousemove(function(e) {
var x = e.pageX;
var y = e.pageY;
$(node).css('left', x);
$(node).css('top', y);
dirtyTriangles = true;
});
$('body').mouseup(function(e) {
$('body').off( "mousemove" );
$('body').off( "mouseup" );
});
}
});
});
var draw = function() {
context.clearRect(0,0,500,500);
var render = function(wireframe, image, tri) {
if (wireframe) {
context.strokeStyle = "black";
context.beginPath();
context.moveTo(tri.p0.x, tri.p0.y);
context.lineTo(tri.p1.x, tri.p1.y);
context.lineTo(tri.p2.x, tri.p2.y);
context.lineTo(tri.p0.x, tri.p0.y);
context.stroke();
context.closePath();
}
if (image) {
drawTriangle(context, image,
tri.p0.x, tri.p0.y,
tri.p1.x, tri.p1.y,
tri.p2.x, tri.p2.y,
tri.t0.u, tri.t0.v,
tri.t1.u, tri.t1.v,
tri.t2.u, tri.t2.v);
}
}
if (dirtyTriangles) {
dirtyTriangles = false;
calculateGeometry();
}
for (triangle of triangles) {
render(true, image, triangle);
}
}
var calculateGeometry = function() {
// clear triangles out
triangles = [];
// generate subdivision
var subs = 7; // vertical subdivisions
var divs = 7; // horizontal subdivisions
var p1 = new Point(parseInt($(controls[0]).css('left')) + 6, parseInt($(controls[0]).css('top')) + 6);
var p2 = new Point(parseInt($(controls[1]).css('left')) + 6, parseInt($(controls[1]).css('top')) + 6);
var p3 = new Point(parseInt($(controls[2]).css('left')) + 6, parseInt($(controls[2]).css('top')) + 6);
var p4 = new Point(parseInt($(controls[3]).css('left')) + 6, parseInt($(controls[3]).css('top')) + 6);
var dx1 = p4.x - p1.x;
var dy1 = p4.y - p1.y;
var dx2 = p3.x - p2.x;
var dy2 = p3.y - p2.y;
var imgW = image.naturalWidth;
var imgH = image.naturalHeight;
for (var sub = 0; sub < subs; ++sub) {
var curRow = sub / subs;
var nextRow = (sub + 1) / subs;
var curRowX1 = p1.x + dx1 * curRow;
var curRowY1 = p1.y + dy1 * curRow;
var curRowX2 = p2.x + dx2 * curRow;
var curRowY2 = p2.y + dy2 * curRow;
var nextRowX1 = p1.x + dx1 * nextRow;
var nextRowY1 = p1.y + dy1 * nextRow;
var nextRowX2 = p2.x + dx2 * nextRow;
var nextRowY2 = p2.y + dy2 * nextRow;
for (var div = 0; div < divs; ++div) {
var curCol = div / divs;
var nextCol = (div + 1) / divs;
var dCurX = curRowX2 - curRowX1;
var dCurY = curRowY2 - curRowY1;
var dNextX = nextRowX2 - nextRowX1;
var dNextY = nextRowY2 - nextRowY1;
var p1x = curRowX1 + dCurX * curCol;
var p1y = curRowY1 + dCurY * curCol;
var p2x = curRowX1 + (curRowX2 - curRowX1) * nextCol;
var p2y = curRowY1 + (curRowY2 - curRowY1) * nextCol;
var p3x = nextRowX1 + dNextX * nextCol;
var p3y = nextRowY1 + dNextY * nextCol;
var p4x = nextRowX1 + dNextX * curCol;
var p4y = nextRowY1 + dNextY * curCol;
var u1 = curCol * imgW;
var u2 = nextCol * imgW;
var v1 = curRow * imgH;
var v2 = nextRow * imgH;
var triangle1 = new Triangle(
new Point(p1x, p1y),
new Point(p3x, p3y),
new Point(p4x, p4y),
new TextCoord(u1, v1),
new TextCoord(u2, v2),
new TextCoord(u1, v2)
);
var triangle2 = new Triangle(
new Point(p1x, p1y),
new Point(p2x, p2y),
new Point(p3x, p3y),
new TextCoord(u1, v1),
new TextCoord(u2, v1),
new TextCoord(u2, v2)
);
triangles.push(triangle1);
triangles.push(triangle2);
}
}
}
// from http://tulrich.com/geekstuff/canvas/jsgl.js
var drawTriangle = function(ctx, im, x0, y0, x1, y1, x2, y2,
sx0, sy0, sx1, sy1, sx2, sy2) {
ctx.save();
// Clip the output to the on-screen triangle boundaries.
ctx.beginPath();
ctx.moveTo(x0, y0);
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.closePath();
//ctx.stroke();//xxxxxxx for wireframe
ctx.clip();
/*
ctx.transform(m11, m12, m21, m22, dx, dy) sets the context transform matrix.
The context matrix is:
[ m11 m21 dx ]
[ m12 m22 dy ]
[ 0 0 1 ]
Coords are column vectors with a 1 in the z coord, so the transform is:
x_out = m11 * x + m21 * y + dx;
y_out = m12 * x + m22 * y + dy;
From Maxima, these are the transform values that map the source
coords to the dest coords:
sy0 (x2 - x1) - sy1 x2 + sy2 x1 + (sy1 - sy2) x0
[m11 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sy1 y2 + sy0 (y1 - y2) - sy2 y1 + (sy2 - sy1) y0
m12 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (x2 - x1) - sx1 x2 + sx2 x1 + (sx1 - sx2) x0
m21 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx1 y2 + sx0 (y1 - y2) - sx2 y1 + (sx2 - sx1) y0
m22 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (sy2 x1 - sy1 x2) + sy0 (sx1 x2 - sx2 x1) + (sx2 sy1 - sx1 sy2) x0
dx = ----------------------------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (sy2 y1 - sy1 y2) + sy0 (sx1 y2 - sx2 y1) + (sx2 sy1 - sx1 sy2) y0
dy = ----------------------------------------------------------------------]
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
*/
// TODO: eliminate common subexpressions.
var denom = sx0 * (sy2 - sy1) - sx1 * sy2 + sx2 * sy1 + (sx1 - sx2) * sy0;
if (denom == 0) {
return;
}
var m11 = -(sy0 * (x2 - x1) - sy1 * x2 + sy2 * x1 + (sy1 - sy2) * x0) / denom;
var m12 = (sy1 * y2 + sy0 * (y1 - y2) - sy2 * y1 + (sy2 - sy1) * y0) / denom;
var m21 = (sx0 * (x2 - x1) - sx1 * x2 + sx2 * x1 + (sx1 - sx2) * x0) / denom;
var m22 = -(sx1 * y2 + sx0 * (y1 - y2) - sx2 * y1 + (sx2 - sx1) * y0) / denom;
var dx = (sx0 * (sy2 * x1 - sy1 * x2) + sy0 * (sx1 * x2 - sx2 * x1) + (sx2 * sy1 - sx1 * sy2) * x0) / denom;
var dy = (sx0 * (sy2 * y1 - sy1 * y2) + sy0 * (sx1 * y2 - sx2 * y1) + (sx2 * sy1 - sx1 * sy2) * y0) / denom;
ctx.transform(m11, m12, m21, m22, dx, dy);
// Draw the whole image. Transform and clip will map it onto the
// correct output triangle.
//
// TODO: figure out if drawImage goes faster if we specify the rectangle that
// bounds the source coords.
ctx.drawImage(im, 0, 0);
ctx.restore();
};
// point class
var Point = function(x,y) {
this.x = x?x:0;
this.y = y?y:0;
}
var p = Point.prototype;
p.length = function(point) {
point = point?point:new Point();
var xs =0, ys =0;
xs = point.x - this.x;
xs = xs * xs;
ys = point.y - this.y;
ys = ys * ys;
return Math.sqrt( xs + ys );
}
var TextCoord = function(u,v) {
this.u = u?u:0;
this.v = v?v:0;
}
var Triangle = function(p0, p1, p2, t0, t1, t2) {
this.p0 = p0;
this.p1 = p1;
this.p2 = p2;
this.t0 = t0;
this.t1 = t1;
this.t2 = t2;
}
【讨论】：
-
这已经非常棒了。然而，当关闭线框时，您可以看到三角形之间的小间距，就像轮廓刚刚变成透明而不是黑色一样。有什么可以做的吗？
-
我认为工件只是精度错误。您可以向三角形镶嵌添加小值，以使它们稍微重叠。此外，您可以使用更少的三角形，但 3d 效果就不那么精确了。
-
感谢您的回复。我尝试重叠三角形，但我的数学理解似乎仅限于真正知道我需要适应什么才能实现它...... ;-) 不过我会再试一次。
-
有没有成功让三角形齐平？
-
@AndyPoes 你能更新小提琴的链接吗？它不工作
最简单的方法是在绘制图像之前对画布应用变换。
http://www.whatwg.org/specs/web-apps/current-work/multipage/the-canvas-element.html#transformations
通过倾斜变换，您可以使它看起来像透视图
这是一个非常简单的例子：
ctx.setTransform (1, -0.2, 0, 1, 0, 0);
ctx.drawImage(blah);
【讨论】：
-
setTransform 允许您指定一个 2 x 3 矩阵。要进行正确的透视（不是等距或正交），您需要 4 x 4，不是吗？
-
哦，你是对的。对不起。不过，已经有一些骇人听闻的尝试。见这里：tulrich.com/geekstuff/canvas/perspective.html
你可以试试function transferPoint (xI, yI, source, destination)解释here。
源和目标是源矩形和目标矩形的四个点。该代码适用于 (SVG) 路径坐标（曲线和直线），但经过一些修改后也适用于像素。
【讨论】：
上面的一些评论者询问了隐藏三角形 - 这样做，它们会消失（信息：@erbridge，@Constantin Groß）：
以下内容的所有功劳归于@AndyPoes，因为这都是他的建议 - 我只是添加他建议的完整版本。
改变这一行：
render(true, image, triangle);
到这里：
render(false, image, triangle);
...黑色三角形会消失，但您会看到三角形之间的间隙，所以现在执行以下操作：
改变这个：
var triangle1 = new Triangle(
new Point(p1x, p1y),
new Point(p3x, p3y),
new Point(p4x, p4y),
new TextCoord(u1, v1),
new TextCoord(u2, v2),
new TextCoord(u1, v2)
);
var triangle2 = new Triangle(
new Point(p1x, p1y),
new Point(p2x, p2y),
new Point(p3x, p3y),
new TextCoord(u1, v1),
new TextCoord(u2, v1),
new TextCoord(u2, v2)
);
改为：
var triangle1 = new Triangle(
new Point(p1x-1, p1y),
new Point(p3x+2, p3y+1),
new Point(p4x-1, p4y+1),
new TextCoord(u1, v1),
new TextCoord(u2, v2),
new TextCoord(u1, v2)
);
var triangle2 = new Triangle(
new Point(p1x-2, p1y),
new Point(p2x+1, p2y),
new Point(p3x+1, p3y+1),
new TextCoord(u1, v1),
new TextCoord(u2, v1),
new TextCoord(u2, v2)
);
....差距将被缩小。
新小提琴 = fiddler off the roof
完整代码在这里：
var controls = [];
var canvas;
var context;
var image;
var triangles = [];
var dirtyTriangles = false;
var rand = function(s,e) {
return Math.random() * (e-s) + s;
}
// dom ready
$(document).ready(function() {
image = new Image();
$(image).load(function() {
setInterval(draw, 1000 / 60);
});
$(image).attr('src', 'https://images.unsplash.com/photo-1500964757637-c85e8a162699?ixlib=rb-1.2.1&q=80&fm=jpg');
canvas = document.createElement('canvas');
$(canvas).attr('width', 500);
$(canvas).attr('height', 500);
$('body').append(canvas);
context = canvas.getContext('2d');
//
for (var i = 0; i < 4; ++i) {
var control = document.createElement('div');
$(control).addClass('node');
$('body').append(control);
controls.push(control);
}
$(controls[0]).css('left', rand(25, 225));
$(controls[0]).css('top', rand(25, 225));
$(controls[1]).css('left', rand(250, 475));
$(controls[1]).css('top', rand(25, 225));
$(controls[2]).css('left', rand(250, 475));
$(controls[2]).css('top', rand(250, 475));
$(controls[3]).css('left', rand(25, 225));
$(controls[3]).css('top', rand(250, 475));
$('body').mousedown(function(e) {
if ($(e.target).hasClass('node')) {
var node = e.target;
$('body').mousemove(function(e) {
var x = e.pageX;
var y = e.pageY;
$(node).css('left', x);
$(node).css('top', y);
dirtyTriangles = true;
});
$('body').mouseup(function(e) {
$('body').off( "mousemove" );
$('body').off( "mouseup" );
});
}
});
});
var draw = function() {
context.clearRect(0,0,500,500);
var render = function(wireframe, image, tri) {
if (wireframe) {
context.strokeStyle = "black";
context.beginPath();
context.moveTo(tri.p0.x, tri.p0.y);
context.lineTo(tri.p1.x, tri.p1.y);
context.lineTo(tri.p2.x, tri.p2.y);
context.lineTo(tri.p0.x, tri.p0.y);
context.stroke();
context.closePath();
}
if (image) {
drawTriangle(context, image,
tri.p0.x, tri.p0.y,
tri.p1.x, tri.p1.y,
tri.p2.x, tri.p2.y,
tri.t0.u, tri.t0.v,
tri.t1.u, tri.t1.v,
tri.t2.u, tri.t2.v);
}
}
if (dirtyTriangles) {
dirtyTriangles = false;
calculateGeometry();
}
for (triangle of triangles) {
render(true, image, triangle);
}
}
var calculateGeometry = function() {
// clear triangles out
triangles = [];
// generate subdivision
var subs = 7; // vertical subdivisions
var divs = 7; // horizontal subdivisions
var p1 = new Point(parseInt($(controls[0]).css('left')) + 6, parseInt($(controls[0]).css('top')) + 6);
var p2 = new Point(parseInt($(controls[1]).css('left')) + 6, parseInt($(controls[1]).css('top')) + 6);
var p3 = new Point(parseInt($(controls[2]).css('left')) + 6, parseInt($(controls[2]).css('top')) + 6);
var p4 = new Point(parseInt($(controls[3]).css('left')) + 6, parseInt($(controls[3]).css('top')) + 6);
var dx1 = p4.x - p1.x;
var dy1 = p4.y - p1.y;
var dx2 = p3.x - p2.x;
var dy2 = p3.y - p2.y;
var imgW = image.naturalWidth;
var imgH = image.naturalHeight;
for (var sub = 0; sub < subs; ++sub) {
var curRow = sub / subs;
var nextRow = (sub + 1) / subs;
var curRowX1 = p1.x + dx1 * curRow;
var curRowY1 = p1.y + dy1 * curRow;
var curRowX2 = p2.x + dx2 * curRow;
var curRowY2 = p2.y + dy2 * curRow;
var nextRowX1 = p1.x + dx1 * nextRow;
var nextRowY1 = p1.y + dy1 * nextRow;
var nextRowX2 = p2.x + dx2 * nextRow;
var nextRowY2 = p2.y + dy2 * nextRow;
for (var div = 0; div < divs; ++div) {
var curCol = div / divs;
var nextCol = (div + 1) / divs;
var dCurX = curRowX2 - curRowX1;
var dCurY = curRowY2 - curRowY1;
var dNextX = nextRowX2 - nextRowX1;
var dNextY = nextRowY2 - nextRowY1;
var p1x = curRowX1 + dCurX * curCol;
var p1y = curRowY1 + dCurY * curCol;
var p2x = curRowX1 + (curRowX2 - curRowX1) * nextCol;
var p2y = curRowY1 + (curRowY2 - curRowY1) * nextCol;
var p3x = nextRowX1 + dNextX * nextCol;
var p3y = nextRowY1 + dNextY * nextCol;
var p4x = nextRowX1 + dNextX * curCol;
var p4y = nextRowY1 + dNextY * curCol;
var u1 = curCol * imgW;
var u2 = nextCol * imgW;
var v1 = curRow * imgH;
var v2 = nextRow * imgH;
var triangle1 = new Triangle(
new Point(p1x-1, p1y),
new Point(p3x+2, p3y+1),
new Point(p4x-1, p4y+1),
new TextCoord(u1, v1),
new TextCoord(u2, v2),
new TextCoord(u1, v2)
);
var triangle2 = new Triangle(
new Point(p1x-2, p1y),
new Point(p2x+1, p2y),
new Point(p3x+1, p3y+1),
new TextCoord(u1, v1),
new TextCoord(u2, v1),
new TextCoord(u2, v2)
);
triangles.push(triangle1);
triangles.push(triangle2);
}
}
}
// from http://tulrich.com/geekstuff/canvas/jsgl.js
var drawTriangle = function(ctx, im, x0, y0, x1, y1, x2, y2,
sx0, sy0, sx1, sy1, sx2, sy2) {
ctx.save();
// Clip the output to the on-screen triangle boundaries.
ctx.beginPath();
ctx.moveTo(x0, y0);
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.closePath();
//ctx.stroke();//xxxxxxx for wireframe
ctx.clip();
/*
ctx.transform(m11, m12, m21, m22, dx, dy) sets the context transform matrix.
The context matrix is:
[ m11 m21 dx ]
[ m12 m22 dy ]
[ 0 0 1 ]
Coords are column vectors with a 1 in the z coord, so the transform is:
x_out = m11 * x + m21 * y + dx;
y_out = m12 * x + m22 * y + dy;
From Maxima, these are the transform values that map the source
coords to the dest coords:
sy0 (x2 - x1) - sy1 x2 + sy2 x1 + (sy1 - sy2) x0
[m11 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sy1 y2 + sy0 (y1 - y2) - sy2 y1 + (sy2 - sy1) y0
m12 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (x2 - x1) - sx1 x2 + sx2 x1 + (sx1 - sx2) x0
m21 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx1 y2 + sx0 (y1 - y2) - sx2 y1 + (sx2 - sx1) y0
m22 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (sy2 x1 - sy1 x2) + sy0 (sx1 x2 - sx2 x1) + (sx2 sy1 - sx1 sy2) x0
dx = ----------------------------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
sx0 (sy2 y1 - sy1 y2) + sy0 (sx1 y2 - sx2 y1) + (sx2 sy1 - sx1 sy2) y0
dy = ----------------------------------------------------------------------]
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
*/
// TODO: eliminate common subexpressions.
var denom = sx0 * (sy2 - sy1) - sx1 * sy2 + sx2 * sy1 + (sx1 - sx2) * sy0;
if (denom == 0) {
return;
}
var m11 = -(sy0 * (x2 - x1) - sy1 * x2 + sy2 * x1 + (sy1 - sy2) * x0) / denom;
var m12 = (sy1 * y2 + sy0 * (y1 - y2) - sy2 * y1 + (sy2 - sy1) * y0) / denom;
var m21 = (sx0 * (x2 - x1) - sx1 * x2 + sx2 * x1 + (sx1 - sx2) * x0) / denom;
var m22 = -(sx1 * y2 + sx0 * (y1 - y2) - sx2 * y1 + (sx2 - sx1) * y0) / denom;
var dx = (sx0 * (sy2 * x1 - sy1 * x2) + sy0 * (sx1 * x2 - sx2 * x1) + (sx2 * sy1 - sx1 * sy2) * x0) / denom;
var dy = (sx0 * (sy2 * y1 - sy1 * y2) + sy0 * (sx1 * y2 - sx2 * y1) + (sx2 * sy1 - sx1 * sy2) * y0) / denom;
ctx.transform(m11, m12, m21, m22, dx, dy);
// Draw the whole image. Transform and clip will map it onto the
// correct output triangle.
//
// TODO: figure out if drawImage goes faster if we specify the rectangle that
// bounds the source coords.
ctx.drawImage(im, 0, 0);
ctx.restore();
};
// point class
var Point = function(x,y) {
this.x = x?x:0;
this.y = y?y:0;
}
var p = Point.prototype;
p.length = function(point) {
point = point?point:new Point();
var xs =0, ys =0;
xs = point.x - this.x;
xs = xs * xs;
ys = point.y - this.y;
ys = ys * ys;
return Math.sqrt( xs + ys );
}
var TextCoord = function(u,v) {
this.u = u?u:0;
this.v = v?v:0;
}
var Triangle = function(p0, p1, p2, t0, t1, t2) {
this.p0 = p0;
this.p1 = p1;
this.p2 = p2;
this.t0 = t0;
this.t1 = t1;
this.t2 = t2;
}
【讨论】：