Is the volume of the parabola y = (x ^ 2) / 4, rotated around the y-axis, delimited by the plane y = 2, equal to 8pi?

I tried to do this through integration (Washer method) and I got 8pi, but I'm not sure if it's correct. If it is wrong, how do you do it correctly?

2d: help needed to fire bullets with interpolation from a rotated rectangle (playable example included + TS / JS code)

You can play a trial version here. (use arrows and & # 39; f & # 39; to shoot)

My bullets are in bad shape. I am learning about interpolations, and my math is not amazing. I am trying to adapt the interpolation code of a book. The example is to interpolate along an axis.

I really don't know how this should work for my case of a bullet shot from a rotating rectangle. If you disable the if block, interpolation is disabled, but the bullets still do not fly directly from the center of the rectangle once it rotates from the starting position.

The bullet is launched from the class & # 39; hero & # 39 ;, which is the rotating rectangle.

Whatever the rotation of the rectangle at the point of pressing fire, it is sent to the bullet class and launched at the same angle. That's all for the math. Can I keep it that simple and add interpolation?

export class Bullet extends VectorCharacter {
  public widthHeight: Vector2 = (6, 25);
  public color = 'black';

  // Add smoothstep
  public totalFrames = 60;
  public frameCounter = 0;
  public startValue = this.y;
  public endValue = 200;
  public smoothstep = (x: number) => x * x * (3 - 2 * x);

  public constructor(public position: Vector2, public rotation: number) {

  public updatePosition(): void {
    // Add smoothstep
    // Run the animation while `frameCounter` is less than `totalFrames`
    if (this.frameCounter < this.totalFrames) {
      // Find the normalized time value
      let normalizedTime = this.frameCounter / this.totalFrames;
      // Apply the easing function
      let curvedTime = this.smoothstep(normalizedTime);
      // Interpolate the sprite's y position based on the curved time
      this.position(1) =
        this.endValue * curvedTime + this.startValue * (1 - curvedTime);

      // Add 1 to the frame counter
      this.frameCounter += 1;

    this.position = vectors.add(this.position, (
      1 * Math.sin(this.rotation * (Math.PI / 180)),
      -1 * Math.cos(this.rotation * (Math.PI / 180)),

You can look at the vector object renderer here (and any other code in the src directory):

I'm confused on how the startValue Y endValue are intended to interact with the sin Y cos functions I don't have a calculated destination, the bullet simply fires forward. CHEERS!

Animation: Can the armor bone not be rotated in Unity when I am trying to rotate its chest towards its target direction?

I want to rotate my character's chest so that the direction of the view is seen correctly.

But I think the animation driver will not let me.

I registered its rotation before and after configuring it, and after configuring it, it is correct, but the next frame before configuring it, has always gone back.

How could I make the animation of my character transform, depending on its orientation?

This is the code:

Debug.Log (Chest.localRotation.eulerAngles);
Chest.localRotation = Quaternion.Euler (90, 90, 0);
Debug.Log (Chest.localRotation.eulerAngles);

Collision detection between rectangles rotated in javascript

Is there a function that can detect collisions between 2 rectangles rotated in javascript?

rectColl function (rect1, rect2) {
back crashing

Why is Lightroom crushing my rotated photos?

I have occasionally seen an error in which the LR JPEG preview is not synchronized with the actual rotation of an image (used in RAW). Usually, you can rotate the photo and then rotate it backwards, and the problem will be solved.

If that does not solve the problem, then you have found an error in the way a particular camera writes its EXIF ​​tags (or maybe an error in the way the Lightroom application interprets those tags). If so, you must report it to Adobe and hope that it is finally solved.

In the meantime, you can probably use exiftool or some other similar tool to adjust the EXIF ​​image rotation metadata for LR to do the right thing, although I could not tell you exactly what to change from the top of my head without seeing what. Camera tags written in your files (and maybe not even then).

Equation of rotated surface

I would like to determine the equation of a disk rotated around the z-axis to $ theta $ angle. Could you tell me how to start?

The equation of the disk is.

$$ (y-a) ^ 2 + (z-a) ^ 2 <= r ^ 2 $$

Could you tell me how to start the problem?

screen: horizontal lines appear wavy when scrolling on the IPS monitor rotated

I am connecting an Acer monitor (CB271HU bmidprx 27 "IPS 2K) connected via DisplayPort to my 13 & # 39; & # 39; 2017 MBP (graphics card: Intel Iris Plus Graphics 640 1536 MB) .When I rotate the monitor vertically (rotation of 90 degrees), I notice that the lines do not update at the same speed horizontally.They seem to be wavy when I move up and down.I recorded the screen when I scroll through an image here.It seems that the left half of the rotated screen is delayed behind the right half.

calculation – Find the volume of a solid rotated around the x-axis

$ y = x ^ 3, y = x, x geq 0 $

$$ begin {align}
V & = int_ {0} ^ {1} A (x) dx = int_ {0} ^ {1} pi (xx ^ 3) ^ 2dx = pi int_ {0} ^ {1} (x ^ 2-2x ^ 4 + x ^ 6) dx \
& = pi bigg[ frac{1}{3}x^3 – frac{2}{5}x^5 + frac{1}{7}x^7bigg]0 <1>
end {align} $$

The response of the book says that the answer is $ frac {4 pi} {21} $ But I'm not getting close to that.

I think there are three main areas in which I checked that I could have ruined, but I do not see anything.
1) configuration
2) integration
3) get the volume

Here is a view of how the graph looks and the area that I am trying to integrate.
enter the description of the image here

How to verify the collisions between a rotated rectangle and a straight line?

How do I detect collisions between a rotated rectangle and a straight line?

geometry of the numbers: What lattices can be rotated in your copy to scale?

Leave $ L = { sum_i n_iv_i mid n_i in mathbb Z } $ be something lattice generated $ d $ independent vectors $ (v_i) _1 ^ d $ since $ mathbb R ^ d $. Call $ L $ rotary If for some scalar multiple of some orthogonal transformation, $ M $, we have $ M (L) subset L $. For example, $ mathbb Z ^ d $ it is rotating, and that's how it is $ {n_1 (1,0) + n_2 (0, sqrt 2) } $, but $ {n_1 (1,0) + n_2 (0, pi) } $ It is not. I am sure that this is a well-known notion with several equivalent definitions, but I could not find anything, so I would appreciate any suggestions or results about them.