I have a polygon (RED SQUARE), for simplicity its a square 100x100 with an offset of 100 from the top left. Assume the coordinate system top left is 0,0. So the coordinates for my simple square are: [x:100,y:100],[x:100,y:200],[x:200,y:200], [x:200,y: 100].
Now lets say I have another square (BLUE SQUARE), its a 100x100 square also, with the same 100 offset from the top left, but this square is rotated 45 degrees, so its cords are: (rounded) [x:150,y:79],[x:79,y:150],[x:150,y:221],[x:221,y:150].
How do I calculate the rotation of BLUE SQUARE (45 degrees) if I am given only the coordinates? Assuming I want the right angles to be straight (vertical or horizontal) in this coordinate system (Like RED SQAURE).
Worded another way... Given these coordinates: [x:150,y:79],[x:79,y:150],[x:150,y:221],[x:221,y:150] how do I calculate the rotation to apply to polygon so its coordinates are this: [x:100,y:100],[x:100,y:200],[x:200,y:200], [x:200,y: 100]
Here is a image demonstrating what I am talking about.
Image of both polygons with coordinates
The way you do this is to
calculate the angle between two adjacent points. The formula for this Math.atan2(x2-x1, y2-y1); This will give you the angle the quadrilateral is on.
Rotate the quadrilateral (from its center) by -angle (or by pi/2 - angle) and one side will be horizontal and one will be vertical
Related
I have the following img that I'd like to drag (by dragging a circle on top of rectangle) and rotate an image.
When dragging, I just want to rotate an image inside the rectangle and not the rectangle itself. I'm not sure I'm doing this correctly, I have this formula when I start dragging:
const newAngle = Math.atan(circleDrag.y, circleDrag.x) * (180 / Math.PI);
I'm getting the position of the circle from the top of the rectangle, but it's giving me something between 90 to 110 degrees only. Correct way of rotation angle would start from 0 I think, and should rotate between 0-360 degrees.
Could somebody direct me on how to calculate rotation angle?
If I understand your needs right, you have to measure angle of direction from the center point of rectangle to the circle center.
Math.atan(circleDrag.y - rectangleCenter.y, circleDrag.x - rectangleCenter.x)
(At this moment you are calculating direction from coordinate origin to the circle)
In the example in Leaflet (for non geographic image), they set "bounds". I am trying to understand how they computed the values
var bounds = [[-26.5,-25], [1021.5,1023]];
The origin is bottom-left and y increases upwards / x towards the right. How did negative numbers turn up here? Also, after experimentation, I see that the actual pixel coordinates change if you specify different coordinates for bounds. I have a custom png map which I would like to use but I am unable to proceed due to this.
Oh, you mean this image:
If you open the full file (available at https://github.com/Leaflet/Leaflet/blob/v1.4.0/docs/examples/crs-simple/uqm_map_full.png ) with an image editor, you'll see that it measures 2315x2315 pixels. Now, the pixel that represents the (0,0) coordinate is not at a corner of the image, but rather 56 pixels away from the lower-left corner of the image:
Similarly, the (1000, 1000) coordinate is about 48 pixels from the top-right corner of the image:
Therefore, if we measure pixel coordinates of the grid corners:
Game coordinate (0, 0) → Pixel coordinate (59, 56)
Game coordinate (1000, 1000) → Pixel coordinate (2264, 2267)
The problem here is finding the bounds (measured in game coordinates) of the image. Or, in other words:
Pixel coordinate (0, 0) → Game coordinate (?, ?)
Pixel coordinate (2315, 2315) → Game coordinate (?, ?)
We know that the pixel-to-game-coordinate ratio is constant, we know the image size and the distance to the coordinates grid, so we can infer stuff:
1000 horizontal game units = image width - left margin - right margin
or
1000 horizontal game units = 2315px - 56px - 48px = 2213px
therefore the pixel/game unit ratio is
2213px / 1000 game units = 2.213 px/unit
therefore the left margin is...
~59px = ~59px / (2.213px/unit) ~= 26.66 game units
...therefore the left edge of the image is at ~ -26.66 game units. Idem for the right margin...
~51px = ~51px / (2.213px/unit) = ~23.04 game units
...therefore the right edge of the image is at ~1023.04 game units
Repeating that for the top and bottom margins we can fill up all the numbers:
Pixel coordinate (0, 0) → Game coordinate (-26.66, -25)
Pixel coordinate (2315, 2315) → Game coordinate (1023.04, 1025)
Why don't these numbers match the ones in the example exactly? Because I might have used a different pixel for measurement when I wrote that Leaflet tutorial. Still, the error is negligible.
Let me remark a sentence from that tutorial:
One common mistake when using CRS.Simple is assuming that the map units equal image pixels. In this case, the map covers 1000x1000 units, but the image is 2315x2315 pixels big. Different cases will call for one pixel = one map unit, or 64 pixels = one map unit, or anything. Think in map units in a grid, and then add your layers (L.ImageOverlays, L.Markers and so on) accordingly.
If you have your own game map (or anything else), you should ask yourself: Where is the (0,0) coordinate? What are the coordinates of the image edges in the units I'm gonna use?
I have a large array of x and y coordinates from which I'm drawing an SVG polygon. For some points, the change in gradient of the line is very small, but I'm still getting a jagged "corner" where the two lines meet. How can I make it have smoothed out corners?
Preferably, this wouldn't kick in when the change in gradient is large (a 90 degree angle for example). So, one polygon could have some corners smoothed out, but where the angle is very different to 180 (180 = no change in gradient), the corners would remain sharp.
I have a shape, a polygon. I have the x,y coordinates of the edges of this polygon.
I'd like to draw 50 circles of 10 pixel radius randomly in this shape.
How do I randomly choose a position in my polygon?
I'm doing this in canvas with javascript, but I don't need any actual code. Maybe some math equations or some direction would be enough
You'd get the whole area of the polygon , apply a rand function on it and draw the circles, if you need to avoid intersection you could create a 'collision' function. Perhaps this helps:
Set: https://en.wikipedia.org/wiki/Set_%28mathematics%29
Calculating the area of a polygon: http://www.wikihow.com/Calculate-the-Area-of-a-Polygon
I have a problem with Raphael.Freetransform. I need the coordinates of the four corners of a rectangle. Unfortunately it is not possible to simply use the x,y,width and height attributes of the rectangle after a transformation, because they still have the data of before.
With rectangle.matrix.x(x,y) and rectangle.matrix.y(x,y) I can receive the real x and y coordinates of the top left corner and with rectangle.attrs.scale.x and rectangle.attrs.scale.y I can calculate the changed width and height of the rectangle.
Now I do need the center coordinates of the transformed and shifted rectangle to calculate with the help of the rotation angle the other corners, but unfortunately the rectangle.attrs.center.x function of Raphael.FreeTransform only returns the initial center of the rectangle.
So how can I get the coordinates of the center of the rotated and shifted rectangle?
Thank you in advance!
In the local coordinate system of the element, the center is at x+width/2, y+height/2, under the assumption that the rectangle goes from (x,y) to (x+width, y+height). So you have to find the coordinates in the global system using the matrix functions.