I want to reproduce the animation here in manim.
I found how to have multiple dots move along a circle, but they only do one turn and don't have constant speed.
How to have them move at constant speed and do multiple turns ?
Here is my attempt up to now :
def construct(self):
circle = Circle()
points = Group(*[Dot((1, 0, 0)) for _ in range(2)])
self.add(circle)
self.add(points)
self.play(
MoveAlongPath(points[0], circle, run_time=1),
MoveAlongPath(points[1], circle, run_time=2)
)
Just found an answer, easier than I thought :
self.play(Rotating(points[0],
radians=2 * TAU,
about_point=ORIGIN),
Rotating(points[1],
radians=TAU,
about_point=ORIGIN),
)
Related
There is a grouped angle (two lines and a arc) moving and rotating at the same time, depending on the location of another Dot, from the video, the grouped angle is lagged behind the Dot, don't know why? below is the code:
class MovRot(Scene):
def construct(self):
ln = Line(LEFT*2, LEFT*1+UP*1.5)
self.add(ln)
ln_ab = Line(LEFT*2, interpolate(LEFT*2, LEFT*1+UP*1.5, 0.7), color=RED_D)
ln_bc = Line(LEFT*2, ORIGIN, color=RED_D)
arc_b = Arc(0, ln_ab.get_angle(), radius=0.6, color=RED_D).move_arc_center_to(LEFT*2)
grp_b = VGroup(ln_ab, ln_bc, arc_b)
self.add(grp_b)
dt = Dot(color=YELLOW_D).move_to(LEFT*2)
grp_1 = grp_b.copy()
def update_grp1(mob, alpha):
mob.become(grp_1)
mob.move_to(dt.get_center(), aligned_edge=arc_b.get_arc_center())
mob.rotate(alpha*PI, about_point=arc_b.get_arc_center())
self.add(grp_1, dt)
self.play(UpdateFromAlphaFunc(grp_b, update_grp1, rate_func=smooth), dt.move_to, LEFT*1+UP*1.5,
rate_func=smooth,
run_time=2)
Thanks for any help.
You always have to write the "master" animation at the beginning of the play method, in your case, the animation that "takes the baton" is move_to, so it must be the first to be written:
self.play(
dt.move_to, LEFT*1+UP*1.5,
UpdateFromAlphaFunc(grp_b, update_grp1, rate_func=smooth),
rate_func=smooth,
run_time=2
)
I know that whenever we want to apply a series of transform at once to a point, we have to specify the sequence in the opposite direction to what we want to perceive. If I want to translate(T) and then rotate(R) a point x we need to end with a concatenation matrix RT, then every point is transformed as (RT)x.
Apple Transform documentation shows that CGAffineTransform work as a transpose version of the above expression. i.e instead of transform a points as Ax for A being any transform matrix they do it as xB for B being the transpose of A.
Also CGAffineTransform.concatenating(T2) documentation state that it stack transforms to the right, ending in an transform matrix of the form as T1 * T2.
Now what are my concerns? If want a series of transformation that translate(T) and then rotate(R), I can call T.concatenating(R) which result in a transform TR, then the points are transformed as xTR, it seem that the order must be respected, but actually I'm getting the wrong result(at least that's what i think), I expect the image A but getting B,
It seem that they are transforming points as TRx, but this contradict the documentation and also not match the result when you apply the transform TR to a point as CGPoint.applying(TR) which also is consistent with the order xTR.
why's that? there's something that I'm missing about how transforms works in iOS?
It's hard to see what the question is here, because you've already answered it. Basically, the order you must use when calling concatenating is the opposite of the order you would use when chaining transformations. Thus for example:
v2.transform =
CGAffineTransform(rotationAngle: 45 * .pi/180).translatedBy(x: 100, y: 0)
In this screen shot, v2 is the green view, and started out where the purple view is:
If you wanted to do that with concatenating, you'd say:
let r = CGAffineTransform(rotationAngle: 45 * .pi/180)
let t = CGAffineTransform(translationX:100, y:0)
v2.transform = t.concatenating(r) // not r.concatenating(t)
If I'm not mistaken, your confusion lies not with order of operations, but with the rotate transformation. Rotation does not take place about the object's center, but about the origin of the frame, which remains fixed in place. When you rotate an object not centered at the frame's origin, it pivots around like the end of the hand of a clock. To achieve image A, you must
Translate your object so that the point you wish to rotate it about (presumably its center) lies at the origin.
Rotate the object.
Translate it to the desired position.
let rotationAngle = CGFloat.pi / 4
let slidingLength : CGFloat = 50
let duration = 0.3
UIView.animate(withDuration: duration) { [weak self] in
self?.slidingView.transform = CGAffineTransform(rotationAngle: rotationAngle)
self?.slidingView.center.x += slidingLength
}
I try use lookat function rotate camera with pan gesture. I use swift and Metal(in this case Metal work the same with OpenGLES). Here is my code
The lookat function:
let kEye = V3f(0.0, 0.0, -2.0)
var ktarget = V3f(0.0, 0.0, 0.0)
let kUp = V3f(0.0, 1.0, 0.0)
var viewMatrix = lookAt(kEye, center: ktarget, up: kUp)
The pan gesture:
func pan(panGesture: UIPanGestureRecognizer){
if panGesture.state == UIGestureRecognizerState.Changed{
let pointInView = panGesture.locationInView(self.view)
let xDelta = (lastPanLocation.x - pointInView.x)/self.view.bounds.width * panSensivity
let yDelta = (lastPanLocation.y - pointInView.y)/self.view.bounds.height * panSensivity
lastPanLocation = pointInView
var viewDirection = rotationM3f(kUp, angle: Float(-xDelta)) * viewDirection
var toRotateAround = Cross(viewDirection, b: kUp)
viewDirection = rotationM3f(toRotateAround, angle: Float(-yDelta)) * viewDirection
ktarget = kEye + viewDirection
} else if panGesture.state == UIGestureRecognizerState.Began {
lastPanLocation = panGesture.locationInView(self.view)
}
}
At the beginning, it works fine, pan the camera after a while, the viewDirection and toRotateAround vector will become -0.0,-0.0,0.0, when finger move vertically but the camera does not look up and down, Anyone knows what is wrong in the code? Thanks~~~
You only modify the view direction (ktarget in the end) but forget about kUP. Once these 2 vectors become parallel the cross product is zero and everything breaks.
The solution you are looking for is recomputing the kUp vector by using a cross product of viewDirection and toRotateAround.
When using rotations like this you need to think of your data as base vectors and a position (location=kEye, forward=ktarget-keye, up=kUp, right=cross(forward, up)). The base vectors are always perpendicular to each other (I suggest them to be normalized as well) and when you rotate you always rotate one of these vectors around another base vectors and after the rotation you need to recompute the 3rd vector by using a cross product.
So to rotate left or right you would rotate the forward around up and then use a cross product between forward and up to get the right vector. (The right vector here is optional since you do not use it)
To rotate up or down you rotate forward vector around right vector and use a cross product between the forward and right to get the new top vector.
Then for tilting left or right you rotate up around forward and get the right vector with cross product of the 2 used vectors.
If you see the logic you will find out there are always 2 ways of rotating along one axis. For instance to rotate left or right you might as well rotate the right vector around up and find the new forward vector by using a cross product of right and up.
There is a trick though. The procedure described here works great for a free movement such as a flight simulation where you can "tilt". It is not appropriate for a movement such as for a first person shooter where up is always in the center of the screen horizontally (I hope you see the difference). To create this FPS way you actually do need to keep up as (0,1,0) but then forward must never be (0,1,0) but it can be (0.001, 0.09, 0) which is pretty close to looking directly upwards. So as long as you limit the upwards angle to some value you should be fine. There are other ways as well...
I'm trying to make a game where the sprite will always move to the right when hit by an object. However since the Sprite rotates constantly and the zero radians rotates with the Sprite causes my calculated magnitude to go the opposite direction if the sprite is facing left and hits the object. Is there a way to keep the direction of the magnitude always pointing to the right even if the zero is facing left?
// referencePoint = upper right corner of the frame
let rightTriangleFinalPoint:CGPoint = CGPoint(x: referencePoint.x, y: theSprite.position.y)
let theSpriteToReferenceDistance = distanceBetweenCGPoints(theSprite.position, b: referencePoint)
let theSpriteToFinalPointDistance = distanceBetweenCGPoints(theSprite.position, b: rightTriangleFinalPoint)
let arcCosineValue = theSpriteToFinalPointDistance / theSpriteToReferenceDistance
let angle = Double(acos(arcCosineValue))
let xMagnitude = magnitude * cos(angle)
let yMagnitude = (magnitude * sin(angle)) / 1.5
Not sure if this works for you:
I would use an orientation constraint to rotate the sprite. The movement can be done independent from the orientation in that case.
I made an tutorial some time ago: http://stefansdevplayground.blogspot.de/2014/09/howto-implement-targeting-or-follow.html
So I figured out what was going on.
It seems like the angle doesn't rotate with the Sprite like I originally thought and the vector that I am making is working with the code above. THE problem that I had was that I also set the collision bit for the objects which is wrong. If I only set the contact bit for the objects against the sprite the my desired outcome comes true.
In reference to this question
Drawing a line between two points using SceneKit
I'm drawing a line in 3D and want to make it thicker by using this code
func renderer(aRenderer: SCNSceneRenderer, willRenderScene scene: SCNScene, atTime time: NSTimeInterval) {
//Makes the lines thicker
glLineWidth(20)
}
but it doesn't work, iOS 8.2.
Is there another way?
Update
From the docs
https://developer.apple.com/library/prerelease/ios/documentation/SceneKit/Reference/SCNSceneRendererDelegate_Protocol/index.html#//apple_ref/occ/intfm/SCNSceneRendererDelegate/renderer:updateAtTime:
I did add SCNSceneRendererDelegate and a valid line width but still could not get the line width to increase.
You cannot assign any number to glLineWidth().
You can check the range of possible values of glLineWidth()by:
glGetFloatv(GL_LINE_WIDTH_RANGE,sizes);
One crazy idea is to use a cylinder for drawing lines ;). I use it when I want to have nice and controllable lines but I am not aware of a handy OpenGl function to do so.
#G Alexander: here you go my implementation of cylinder. It is a bit tedious but it is what I have at the moment.
If you give me points p0 and p1, Vector normal=(p1-p0).normalize() would be the axis of the cylinder.
pick point p2 that is not on the vector Normal.
q=(p2-p0).normalize();
normal.crossproduct(q)=v0;
normal.crossproduct(v0)=v1;
Having these two vectors you can have circles with any radius that are stacked along the axis of the cylinder using the following function (A cylinder is a stack of circles):
public Circle make_circle(Point center, Vector v0, Vector v1, double radius)
{
Circle c;
for (double i = 0; i < 2 * Math.PI; i += 0.05)
{
Point p = new Point(center + radius * Math.Cos(i) * v0 + radius * Math.Sin(i) * v1);
c.Add(p);
}
return c;
}
You only need to make circles using this function along the axis of the cylinder:
List<Circle> Cylinder = new List<Circle>();
for(double i=0;i<1;i+=0.1)
{
Cylinder.add( make_circle(P0+i*normal, v0, v1,radius);
}
Now you should take two consecutive circles and connect them with quads by sampling uniformly.
I have implemented it this way since I had circles implemented already.
A simpler way to implement is make the circle along the x axis and then rotate and translate it to p0 and make it align with normal or to use gluCylinder if you are the fan of Glu....
Hopefully it works for you.