CODEWITHSUNDEEP
javascriptmathcanvastrigonometry
WesleyJohnson
WesleyJohnson

Reputation: 1538

Calculate x, y coordinates of rotated line segments to draw on a Canvas

This is less an HTML, CANVAS question and more of a general math question. I posted it here because it's prototyped using CANVAS and is still kind of a general programming question that I thought someone could answer. Here is the basic idea: I want to draw a line 10 pixels thick, but I don't want to use the standard lineTo and set a stroke width. I want to actually draw the border of the line using beginPath and lineTo. The reason being is this is actually for AS3 project and using this method allows us to have a line stroke and fill. So rotating the canvas and things of that nature are out of the question. I just need to figure out how to calculate the proper x, y coordinates for the line.

In the code below is the coordinates for the top of a line. I basically want to take this coordinates, add 10 to the y axis for each one and that will give me the return coordinates for the bottom of the line. Of course, each segment of the line is rotated, so calculating the coordinates for the bottom of the line has proved tricky. I'm hoping someone can help.

Once you run the example code, the issue should be obvious. The line isn't drawn properly. For relatively mild rotations of line segments it seems to work, but as the angle of rotation gets more severe the x, y coordinates are calculated incorrectly.

<!doctype html>
<html>
<body>
<canvas id="canvas" width="800" height="600">
</canvas>
<script type="text/javascript">
var coords = [
    {x:78,y:183},
    {x:130,y:183},
    {x:237,y:212},
    {x:450,y:213},
    {x:517,y:25},
    {x:664,y:212},
    {x:716,y:212}
];

var coordsBck = [];

for( i = 0; i < coords.length; i++ ) {
    var c1, c2, r;
    c1 = coords[i];

    if( i < coords.length - 1 ) {
        c2 = coords[i + 1];
        r = Math.atan2((c2.y - c1.y),(c2.x - c1.x));
        console.log( c1.x, c1.y, c2.x, c2.y, ( r * 180/Math.PI ));
    }
    else
    {
        r = 00;
    }
    var d = r * 180/Math.PI;    
    var cos = Math.cos( r );
    var sin = Math.sin( r );

    var x = cos * 0 - sin * 10;
    var y = sin * 0 + cos * 10;
    coordsBck.push({x: c1.x + x, y: c1.y + y});
}

while(coordsBck.length > 0 )
{
    coords.push( coordsBck.pop() );
}

var ctx = document.getElementById("canvas").getContext("2d");
ctx.beginPath();
for( i = 0; i < coords.length; i++ ) {
    var line = coords[i];
    console.log( i, line.x, line.y );
    if( i == 0 )
    {
        ctx.moveTo( line.x, line.y );
    }
    else
    {
        ctx.lineTo( line.x, line.y );
    }
}
ctx.fill();

function t(o) {
    return "x: " + o.x + ", y: " + o.y;
}
</script>
</body>
</html>

Upvotes: 2

Views: 2112

Answers (3)

WesleyJohnson
WesleyJohnson

Reputation: 1538

I ended up sorting this out after Vincent and Sirisian's answers gave me some ideas. I really appreciate the input guys! Basically, both of those answers made me realized I should be treating the segments like rectangles and that I needed some additional coordinates. I put together a jsfiddle if anyone was in interested.

http://jsfiddle.net/WesleyJohnson/sAaM9/1/

Upvotes: 1

Sirisian
Sirisian

Reputation: 447

If you don't need end caps. http://jsfiddle.net/xA6kB/1/

<doctype !html>
<html>
<body>
<canvas id="canvas" width="800" height="600">
</canvas>
<script type="text/javascript">
var points =
[
    {x: 78, y: 183},
    {x: 130, y: 183},
    {x: 237, y: 212},
    {x: 450, y: 213},
    {x: 517, y: 25},
    {x: 664, y: 212},
    {x: 716, y: 212}
];

var quads = [];
var lineThickness = 10;

// Remove the -1 to create a loop
for (var i = 0; i < points.length - 1; ++i)
{
    var point = points[i];
    var nextPoint = points[(i + 1) % points.length];
    // Right hand normal with x positive to the right and y positive down
    var normal = {x: -(nextPoint.y - point.y), y: nextPoint.x - point.x};
    // Normalize normal
    var normalLength = Math.sqrt(normal.x * normal.x + normal.y * normal.y);
    normal.x /= normalLength;
    normal.y /= normalLength;

    // A quad has 4 points
    quads.push({x: point.x - lineThickness / 2 * normal.x, y: point.y - lineThickness / 2 * normal.y});
    quads.push({x: nextPoint.x - lineThickness / 2 * normal.x, y: nextPoint.y - lineThickness / 2 * normal.y});
    quads.push({x: nextPoint.x + lineThickness / 2 * normal.x, y: nextPoint.y + lineThickness / 2 * normal.y});
    quads.push({x: point.x + lineThickness / 2 * normal.x, y: point.y + lineThickness / 2 * normal.y});
}

var context = document.getElementById("canvas").getContext("2d");

context.beginPath();
for(var i = 0; i < quads.length; i += 4)
{
    context.moveTo(quads[i].x, quads[i].y);
    context.lineTo(quads[i + 1].x, quads[i + 1].y);
    context.lineTo(quads[i + 2].x, quads[i + 2].y);
    context.lineTo(quads[i + 3].x, quads[i + 3].y);
}
context.fill();
</script>
</body>
</html>

Upvotes: 1

GameAlchemist
GameAlchemist

Reputation: 19294

When i have such issues, i usually compute normalized vectors, and 'play' with them. Say you draw a line from A to B, compute AB vector (ABx=Bx-Ax ; ABy=By-Ay) then i normalize it (...) to get ABN.

Then i compute ABNR, the 90 degree rotation of ABN ( ABNR.x = -ABN.y ; ABNR.y = ABN.x )

Then in your example, say A' and A'' are the points surrounding A, we have the simple A'=A+5*ABNR and A''= A-5*ABNR , and as well B'=B+5*ABNR and B''=B-5*ABNR. The rectangle you want to draw is the A'A''B''B' rectangle.

There must be much more optimized way to do this (after all, one can draw a line with only additions), this one is simple and works, it depends on your speed rquirements. You may also optimze the code once you have your formulas working.

Upvotes: 1

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