I have made canvas Shapes(squares) in kinetic js having 4 control points on each of their vertices.A user can click and drag these control points and distort the shape any way he/she pleases. I also tried adding control points in the mid-point of each line by adding additional anchors and plugging them into the Bezier Curve..The js fiddle is http://jsfiddle.net/Lucy1/opsy1pn9/4/
The corresponding JS code is
var room = new Kinetic.Shape({
x: 0,
y: 0,
width: w,
height: h,
stroke: "blue",
fill: 'red',
drawFunc: function (context) {
var x = this.x();
var y = this.y();
var w = this.width();
var h = this.height();
var tlX = this.anchorTL.x();
var tlY = this.anchorTL.y();
context.beginPath();
context.moveTo(tlX, tlY);
// top
context.bezierCurveTo(x + w / 3, y, this.anchorTM.x(), this.anchorTM.y(), this.anchorTR.x(), this.anchorTR.y());
// right
context.bezierCurveTo(x + w, y + h / 3, this.anchorRM.x(), this.anchorRM.y(), this.anchorBR.x(), this.anchorBR.y());
// bottom
context.bezierCurveTo(x + w * 2 / 3, y + h, this.anchorBM.x(), this.anchorBM.y(), this.anchorBL.x(), this.anchorBL.y());
// left
context.bezierCurveTo(x, y + h * 2 / 3, this.anchorLM.x(), this.anchorLM.y(), tlX, tlY);
context.closePath();
context.fillStrokeShape(this);
}
});
g.add(room);
room.anchorTR = makeAnchor(w, 0, g);
room.anchorBR = makeAnchor(w, h, g);
room.anchorBL = makeAnchor(0, h, g);
room.anchorTL = makeAnchor(0, 0, g);
room.anchorTM = makeAnchor(w/2,0,g);
room.anchorRM = makeAnchor(w,h/2,g);
room.anchorLM = makeAnchor(0,h/2,g);
room.anchorBM = makeAnchor(w/2,h,g);
layer.draw();
}
The problem i am facing is that the mid-point control points are not moving with the line like the control points situated at the vertex..Please Help.
In looking at the history of your posts, you have previously been using Cubic Bezier Curves.
Each Bezier curve has 4 control points so you need 4 anchors--not 3 as you show. The control points are: (1) starting point (a corner) (2) mid point influencing the starting point (3) mid point influencing the ending point (4) ending point (a corner).
But your fiddle uses just one control point on your curve between the corners. This indicates a Quadratic Curve instead of a Cubic Bezier Curve.
Each Quadratic curve has 3 control points so you need 3 anchors as in your fiddle. The control points are: (1) starting point (a corner) (2) middle control point influencing the curve (3) ending point (a corner).
So if instead you want the user to drag on a quadratic curve to manipulate that curve, you can approximate the resulting middle quadratic control point using this math:
var controlPointX = 2*mouseX -startpointX/2 -endpoinX/2;
var controlPointY = 2*mouseY -startpointY/2 -endpointY/2;
Here's a Demo having the user drag to adjust a Quadratic curve:
http://jsfiddle.net/m1erickson/f4ag0myj/
Related
I'm trying to join two separate bezier curves into one continuous curve. Currently, what I have looks like this:
The problem is that they aren't joined, so the points at which they meet look pointy/sharp instead of curvy and smooth. I've looked into documentation for joining bezier curves in P5.js, but am unsure of how to translate this into HTML5 Canvas. How do I join these two bezier curves so that they look like one smooth and continuous curve?
This is my code:
const canvas = document.getElementById('canvas');
const c = canvas.getContext("2d");
width = 800;
height = 500;
canvas.width = width;
canvas.height = height;
let face;
let centerX = width / 2;
let centerY = height / 3;
setup();
function setup() {
c.clearRect(0, 0, canvas.width, canvas.height);
face = new Face();
draw();
};
function draw() {
setBackground(`rgba(250, 250, 250, 1)`);
c.beginPath();
c.moveTo(centerX - face.hsx, centerY + face.hsy);
c.bezierCurveTo(centerX - face.hcp1x / 10, centerY - face.hsy2,
centerX + face.hcp1x / 10, centerY - face.hsy2,
centerX + face.hsx, centerY + face.hsy);
c.moveTo(centerX - face.hsx, centerY + face.hsy);
c.bezierCurveTo(centerX - face.hcp1x, centerY + face.hcp1y,
centerX + face.hcp1x, centerY + face.hcp1y,
centerX + face.hsx, centerY + face.hsy);
c.stroke();
c.fillStyle = (`rgba(25, 250, 211, 0)`);
c.fill();
}
function setBackground(color) {
c.fillStyle = color;
c.fillRect(0, 0, width, height);
}
function Face() {
this.hsx = 150;
this.hsy = 0;
this.hsy2 = 120;
this.hcp1x = 120;
this.hcp1y = 250;
}
Common tangent
To join two beziers smoothly you need to make the lines from the common point parallel thus defining the tangent at the end and start of the two beziers to be the same.
The following image illustrates this
The line that is defined by the two control points (C2, C1) and the common point (P) is the tangent of the curve at P. The length of the line segments have no constraints.
How?
There are dozens of ways to do this and how you do it is dependent on the requirements of the curve, the type of curve, and much more.
Example
I am not going to give a full example as it requires an understanding of vector maths and a cover all solution on the assumption you are not familiar with vector maths would be huge.
Thus the most basic pseudo code example uses the previous control and end points to calculate the next control point. ? represents unknowns which are not bound by constraints required to keep the lines parallel
// From illustration in answer
corner = ? // Distance to next control point as fraction of distance
// from previous control point
C2 = {x:?, y:?} // Last control point of previous bezier
P = {x:?, y:?} // Start of next bezier
C1 = { // Next control point along line from previous and scaled
x: P.x + (P.x - C2.x) * corner,
y: P.y + (P.y - C2.y) * corner,
}
// two beziers with common point P
ctx.bezierCurveTo(?,?, C2.x, C2.y, P.x, P.y)
ctx.bezierCurveTo(C1.x, C1.y, ?, ?, ?, ?)
In the below page:
https://www.w3schools.com/tags/tryit.asp?filename=tryhtml5_canvas_beziercurveto
You change the width and height of the canvas to 1000.
Then you replace the two lines between beginpath and stroke with the below code.
points=[
{x:0, y:300},//0
{x:100,y:500},//1
{x:200,y:300},//2
{x:300,y:100},//3
{x:400,y:300},//4
{x:100,y:500},//5
{x:100,y:300},//6
];
ctx.rect(points[0].x-5, points[0].y-5, 10,10);
var smoother={};
smoother.x=((points[1].x-points[0].x)/10)+points[0].x;
smoother.y=((points[1].y-points[0].y)/10)+points[0].y;
ctx.rect(smoother.x-5, smoother.y-5, 10,10);
ctx.rect(points[1].x-5, points[1].y-5, 10,10);
ctx.rect(points[2].x-5, points[2].y-5, 10,10);
ctx.moveTo(points[0].x,points[0].y);
ctx.bezierCurveTo(
smoother.x, smoother.y,
points[1].x, points[1].y,
points[2].x, points[2].y
);
var smoother={};
var dx=(points[2].x-points[1].x);
var dy=(points[2].y-points[1].y);
var yperx=(dy/dx);
travel_x=dx;
travel_y=(dx*yperx);
smoother.x=points[2].x+travel_x/3;
smoother.y=points[2].y+travel_y/3;
ctx.rect(smoother.x-5, smoother.y-5, 10,10);
ctx.rect(points[3].x-5, points[3].y-5, 10,10);
ctx.rect(points[4].x-5, points[4].y-5, 10,10);
ctx.moveTo(points[2].x,points[2].y);
ctx.bezierCurveTo(
smoother.x, smoother.y,
points[3].x, points[3].y,
points[4].x, points[4].y
);
var smoother={};
var dx=(points[4].x-points[3].x);
var dy=(points[4].y-points[3].y);
var yperx=(dy/dx);
travel_x=dx;
travel_y=(dx*yperx);
smoother.x=points[4].x+travel_x/3;
smoother.y=points[4].y+travel_y/3;
ctx.rect(smoother.x-5, smoother.y-5, 10,10);
ctx.rect(points[5].x-5, points[5].y-5, 10,10);
ctx.rect(points[6].x-5, points[6].y-5, 10,10);
ctx.moveTo(points[4].x,points[4].y);
ctx.bezierCurveTo(
smoother.x, smoother.y,
points[5].x, points[5].y,
points[6].x, points[6].y
);
You can also run it here by pressing the run button:
https://www.w3schools.com/code/tryit.asp?filename=GSP1RKBFHGGK
At that you can manipulate the pixels in points[], and notice that the bezier curves always connect kinda smoothly.
That's because in each new bezier curve, the system automatically makes the first bezier point, which only serves the role of smoothing the line. Which is basically just a point that continues in whatever direction the previous bezier was heading, for a little bit. The next pixel in the bezier is then an actual destination, which the given bezier curve then takes care of smoothing.
There is the number 3 in there, it represents how quickly you want to start going in the actual direction. If it's too large we start to too quickly head in the needed direction and the smoothness suffers.
If it's too small we are ignoring too much where the line needs to be going, in favor of smoothness.
After saw this question many times and replied with an old (an not usable) code I decide to redo everything and post about it.
Rectangles are defined by:
center : x and y for his position (remember that 0;0 is TOP Left, so Y go down)
size: x and y for his size
angle for his rotation (in deg, 0 deg is following axis OX and turn clockwise)
The goal is to know if 2 rectangles are colliding or not.
Will use Javascript in order to demo this (and also provide code) but I can be done on every language following the process.
Links
Final Demo on Codepen
GitHub repository
Concept
In order to achieve this we'll use corners projections on the other rectangle 2 axis (X and Y).
The 2 rectangles are only colliding when the 4 projections on one rectangles hit the others:
Rect Blue corners on Rect Orange X axis
Rect Blue corners on Rect Orange Y axis
Rect Orange corners on Rect Blue X axis
Rect Orange corners on Rect Blue Y axis
Process
1- Find the rects axis
Start by creating 2 vectors for axis 0;0 (center of rect) to X (OX) and Y (OY) then rotate both of them in order to get aligned to rectangles axis.
Wikipedia about rotate a 2D vector
const getAxis = (rect) => {
const OX = new Vector({x:1, y:0});
const OY = new Vector({x:0, y:1});
// Do not forget to transform degree to radian
const RX = OX.Rotate(rect.angle * Math.PI / 180);
const RY = OY.Rotate(rect.angle * Math.PI / 180);
return [
new Line({...rect.center, dx: RX.x, dy: RX.y}),
new Line({...rect.center, dx: RY.x, dy: RY.y}),
];
}
Where Vector is a simple x,y object
class Vector {
constructor({x=0,y=0}={}) {
this.x = x;
this.y = y;
}
Rotate(theta) {
return new Vector({
x: this.x * Math.cos(theta) - this.y * Math.sin(theta),
y: this.x * Math.sin(theta) + this.y * Math.cos(theta),
});
}
}
And Line represent a slop using 2 vectors:
origin: Vector for Start position
direction: Vector for unit direction
class Line {
constructor({x=0,y=0, dx=0, dy=0}) {
this.origin = new Vector({x,y});
this.direction = new Vector({x:dx,y:dy});
}
}
Step Result
2- Use Rect Axis to get corners
First want extend our axis (we are 1px unit size) in order to get the half of width (for X) and height (for Y) in order to be able by adding when (and inverse) to get all corners.
const getCorners = (rect) => {
const axis = getAxis(rect);
const RX = axis[0].direction.Multiply(rect.w/2);
const RY = axis[1].direction.Multiply(rect.h/2);
return [
rect.center.Add(RX).Add(RY),
rect.center.Add(RX).Add(RY.Multiply(-1)),
rect.center.Add(RX.Multiply(-1)).Add(RY.Multiply(-1)),
rect.center.Add(RX.Multiply(-1)).Add(RY),
]
}
Using this 2 news methods for Vector:
// Add(5)
// Add(Vector)
// Add({x, y})
Add(factor) {
const f = typeof factor === 'object'
? { x:0, y:0, ...factor}
: {x:factor, y:factor}
return new Vector({
x: this.x + f.x,
y: this.y + f.y,
})
}
// Multiply(5)
// Multiply(Vector)
// Multiply({x, y})
Multiply(factor) {
const f = typeof factor === 'object'
? { x:0, y:0, ...factor}
: {x:factor, y:factor}
return new Vector({
x: this.x * f.x,
y: this.y * f.y,
})
}
Step Result
3- Get corners projections
For every corners of a rectangle, get the projection coord on both axis of the other rectangle.
Simply by adding this function to Vector class:
Project(line) {
let dotvalue = line.direction.x * (this.x - line.origin.x)
+ line.direction.y * (this.y - line.origin.y);
return new Vector({
x: line.origin.x + line.direction.x * dotvalue,
y: line.origin.y + line.direction.y * dotvalue,
})
}
(Special thank to Mbo for the solution to get projection.)
Step Result
4- Select externals corners on projections
In order to sort (along the rect axis) all the projected point and take the min and max projected points we can:
Create a vector to represent: Rect Center to Projected corner
Get the distance using the Vector Magnitude function.
get magnitude() {
return Math.sqrt(this.x * this.x + this.y * this.y);
}
Use the dot product to know if the vector is facing the same direction of axis of inverse (where signed distance" is negative)
getSignedDistance = (rect, line, corner) => {
const projected = corner.Project(line);
const CP = projected.Minus(rect.center);
// Sign: Same directon of axis : true.
const sign = (CP.x * line.direction.x) + (CP.y * line.direction.y) > 0;
const signedDistance = CP.magnitude * (sign ? 1 : -1);
}
Then using a simple loop and test of min/max we can find the 2 externals corners. The segment between them is the projection of a Rect on the other one axis.
Step result
5- Final: Do all projections hit rect ?
Using simple 1D test along the axis we can know if they hit or not:
const isProjectionHit = (minSignedDistance < 0 && maxSignedDistance > 0
|| Math.abs(minSignedDistance) < rectHalfSize
|| Math.abs(maxSignedDistance) < rectHalfSize);
Done
Testing all 4 projections will give you the final result. =] !!
Hope this answer will help as many people as possible. Any comments are appreciated.
I've been trying to draw an arc on the canvas, using p5.js. I got start & end points, the chord length i calculate using pythagoras using the two points, the height & width values are also given.
In order to draw an arc, i need to use the following function;
arc(x, y, w, h, start, stop, [mode], [detail]) for docs refer to here
The start & stop parameters refer to the start&stop angles specified in radians. I can't draw the arc without those angles and i'm unable to calculate them using what i got.
I searched for lots of examples similar to my question, but it is suggested to calculate the center angle, which i'm also unable to do so. Even though i was able to calculate the center angle, how i'm supposed to get the start&stop angles afterwards?
I have drawn some example illustrations on GeoGebra;
The angle of a vector can be calculated by atan2().
Note, that:
tan(alpha) = sin(alpha) / cos(alpha)
If you've a vector (x, y), then than angle (alpha) of the vector relative to the x-axis is:
alpha = atan2(y, x);
The start_angle and stop_angle of an arc, where the center of the arc is (cpt_x, cpt_y), the start point is (spt_x, spt_y) and the end point is (ept_x, ept_y), can be calculated by:
start_angle = atan2(spt_y-cpt_y, spt_x-cpt_x);
stop_angle = atan2(ept_y-cpt_y, ept_x-cpt_x);
See the example, where the stop angle depends on the mouse position:
var sketch = function( p ) {
p.setup = function() {
let sketchCanvas = p.createCanvas(p.windowWidth, p.windowHeight);
sketchCanvas.parent('p5js_canvas')
}
p.windowResized = function() {
p.resizeCanvas(p.windowWidth, p.windowHeight);
}
p.draw = function() {
let cpt = new p5.Vector(p.width/2, p.height/2);
let rad = p.min(p.width/2, p.height/2) * 0.9;
let stop_angle = p.atan2(p.mouseY-cpt.y, p.mouseX-cpt.x);
p.background(192);
p.stroke(255, 64, 64);
p.strokeWeight(3);
p.noFill();
p.arc(cpt.x, cpt.y, rad*2, rad*2, 0, stop_angle);
}
};
var circle = new p5(sketch);
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.9.0/p5.js"></script>
<div id="p5js_canvas"></div>
My game has many Laser objects. mx & my represent velocity. I use the following code to draw a line from behind the Laser 2 pixels to ahead of the Laser in the direction it's going 2 pixels.
Removing the first line of the function adjusted the % of the Profiling by ~1% but I don't like the way it looks. I think I could optimize the drawing by sorting by Linewidth but that doesn't appear to get me much.
How else could I optimize this?
Laser.prototype.draw = function(client, context) {
context.lineWidth = Laser.lineWidth;
context.beginPath();
context.moveTo(this.x - this.mx * 2, this.y - this.my * 2);
context.lineTo(this.x + this.mx * 2, this.y + this.my * 2);
context.strokeStyle = this.teamColor;
context.closePath();
context.stroke();
}
Instead of multiplying things by two, why not add them?
E.g.
context.moveTo(this.x - this.mx - this.mx, this.y - this.my - this.my);
context.lineTo(this.x + this.mx + this.mx, this.y + this.my - this.my);
Testing shows that addition is an order of magnitude faster on an imac over multiplication
https://jsfiddle.net/1c85r2pq/
Dont use moveTo or lineTo as they do not use the hardware to render and are very slow. Also your code is drawing the line twice
ctx.beginPath(); // starts a new path
ctx.moveTo(x,y); // sets the start point of a line
ctx.lineTo(xx,yy); // add a line from x,y to xx,yy
// Not needed
ctx.closePath(); // This is not like beginPath
// it is like lineTo and tells the context
// to add a line from the last point xx,yy
// back to the last moveTo which is x,y
This would half the already slow render time.
A quick way to draw lines using bitmaps.
First at the start create an image to hold the bitmap used to draw the line
function createLineSprite(col,width){
var lineSprite = document.createElement("canvas");
var lineSprite.width = 2;
var lineSprite.height = width;
lineSprite.ctx = lineSprite.getContext("2d");
lineSprite.ctx.fillStyle = col;
lineSprite.ctx.fillRect(0,0,2,width);
return lineSprite;
}
var line = createLineSprite("red",4); // create a 4 pixel wide red line sprite
Or you can use an image that you load.
To draw a line you just need to create a transform that points in the direction of the line, and draw that sprite the length of the line.
// draw a line with sprite from x,y,xx,yy
var drawLineSprite = function(sprite,x,y,xx,yy){
var nx = xx-x; // get the vector between the points
var ny = yy-y;
if(nx === 0 && ny === 0){ // nothing to draw
return;
}
var d = Math.hypot(nx,ny); // get the distance. Note IE does not have hypot Edge does
// normalise the vector
nx /= d;
ny /= d;
ctx.setTransform(nx,ny,-ny,nx,x,y); // create the transform with x axis
// along the line and origin at line start x,y
ctx.drawImage(sprite, 0, 0, sprite.width, sprite.height, 0, -sprite.height / 2, d, sprite.height);
}
To draw the line
drawSpriteLine(line,0,0,100,100);
When you are done drawing all the lines you can get the default transform back with
ctx.setTransform(1,0,0,1,0,0);
The sprite can be anything, this allows for very detailed lines and great for game lasers and the like.
If you have many different colours to draw then create one sprite (image) that has many colour on it, then in the line draw function simply draw only the part of the sprite that has the colour you want. You can stretch out a single pixel to any size so you can get many colours on a small bitmap.
I'm trying to find a point that is equal distance away from the middle of a perpendicular line. I want to use this point to create a Bézier curve using the start and end points, and this other point I'm trying to find.
I've calculated the perpendicular line, and I can plot points on that line, but the problem is that depending on the angle of the line, the points get further away or closer to the original line, and I want to be able to calculate it so it's always X units away.
Take a look at this JSFiddle which shows the original line, with some points plotted along the perpendicular line:
http://jsfiddle.net/eLxcB/1/.
If you change the start and end points, you can see these plotted points getting closer together or further away.
How do I get them to be uniformly the same distance apart from each other no matter what the angle is?
Code snippit below:
// Start and end points
var startX = 120
var startY = 150
var endX = 180
var endY = 130
// Calculate how far above or below the control point should be
var centrePointX = ((startX + endX) / 2);
var centrePointY = ((startY + endY) / 2);
// Calculate slopes and Y intersects
var lineSlope = (endY - startY) / (endX - startX);
var perpendicularSlope = -1 / lineSlope;
var yIntersect = centrePointY - (centrePointX * perpendicularSlope);
// Draw a line between the two original points
R.path('M '+startX+' '+startY+', L '+endX+' '+endY);
Generally you can get the coordinates of a normal of a line like this:
P1 = {r * cos(a) + Cx, -r * sin(a) + Cy},
P2 = {-r * cos(a) + Cx, r * sin(a) + Cy}.
A demo applying this to your case at jsFiddle.