unity – Getting array of points shaping curve from 2 vector3 points

What I want is to get path for DoTween method DoPath(), which as a parameter expects array of vectors shaping the direction of the path. I googled some stuff and found out nothing. Just think bezier curve is good idea but i dont even know how it works. Here is an ilustration of my problem

The movement must be curved, don’t need linear one.

Degree \$6\$ curve in \$mathbb{P}^3\$

Let a degree $$6$$ curve $$C$$ is given as $$(Q_1 cap Q_2) cup l^2$$ where $$Q_i’s$$ are qudrics and $$l$$ is a line intersecting $$Q_1 cap Q_2$$. Is it true that $$C$$ always lies on a quadric ?

bitcoin – Public key of Elliptic Curve Digital Signature Algorithm

How do I compute my public key, if my private key for ECDSA in SHA-1 is equals to ab2c34b85dd576112f34?

``````where:
x = 54545578718895168534326250603453777594175500187
y = 35454270510029780865563085577751305070431844712
p = 12121157920892373161954235709850086879078532645

``````

ag.algebraic geometry – Why is this “the first elliptic curve in nature”?

The LMFDB describes the elliptic curve 11a3 (or 11.a3) as “The first elliptic curve in nature”. It has minimal Weierstraß equation
$$y^2 + y = x^3 – x^2.$$
My guess is that there is some problem in Diophantus’ Arithmetica, or perhaps some other ancient geometry problem, that is equivalent to finding a rational point on this curve. What might it be?

fitting – Any way to draw a curve by hand and use the data and fit a function on datas?

I’d like to draw a simple curve by hand.
Next, I have to figure out what function defines it the best.

I’ve been thinking long but I don’t have an idea how to make it.

What I could imagine is that somehow draw series of points with drawing tools and get coordinates and then fit an arbitrary function to the coordinates.

In a similar topic someone suggested to use Classify but I don’t understand how it helps here.

So I don’t know how to start, any idea?

Intersection of the contour diagram curve

How do I show intersection points in a contour diagram? I have 2 graphical functions, but I cannot figure out how to display the points of their intersections.

real analysis – existence of a non-trivial zero curve

Look at the ring-shaped area $$mathcal {A}: = {(r, theta) in mathbb {R} ^ 2: 1 leq r leq 2 }$$. Suppose that $$f: mathcal {A} rightarrow mathbb {R}$$ is a smooth function satisfying $$f | _ {r = 1} <0$$ and $$f | _ {r = 2}> 0$$. Also assume that the zero amount of $$f$$ is a collection of smooth curves. Is it true that there is a component of? $${f = 0 }$$ What winds around the origin?

comment: Continuity of $$f$$ implies that on every curve that connects the outer boundary of $$mathcal {A}$$ at its inner limit there is a zero of $$f$$. However, only this observation does not imply the existence of a zero curve that winds around the origin.

Thank you so much!

Calculus – Calculation of the overestimation of the displacement for the speed curve v (t) = 10 + 5t-t ^ 2 (further information in the body)

I'm a little confused about how I do this question. Link to question here

The question specifies a speed-time function (v (t) = 10 + 5t-t ^ 2) and asks whether the shift should be determined with an overestimation U5 (determination of the overestimation with 5 rectangles). The confusing part, however, is that the question is that the speed is constant after every second interval. This confuses me because f (2) = 16 f (2.5) = 16.25 and f (3) = 16 and I don't know if I should use 16.25 for the overestimation.

Does the picture here exactly show what the overestimation would look like according to the question? or would touch the middle rectangle 16.25 f (2.5) as this is the largest number between the interval 2 and 3. The main co-fusion results from the wording of the question “You have to determine the displacement of the vehicle after 5 seconds by assuming that the speed of the vehicle is over constant
every one second time interval. & # 39;

Read the question carefully and tell me what you think the overrated U5 should be. For me it's either 76 units ^ 2 or 76.25 units ^ 2.

f (1) + f (2) + f (3) + f (3) + f (4) = 76
or
f (1) + f (2) + f (2.5) + f (3) + f (4) = 76.25

differential geometry – straight line curve in a surface (=> planar and geodetic) that is not a line of curvature

I try to create a curve with these requirements, but all straightforward Curve that I get is Line of curvature.

I guess I have to use the fact that the second derivative is 0 because it's straightforward, but I don't know why it takes me so long to find one.

Curve that describes all possible points C, where points A and B and the ratio of their distances to C are known

I know the points A and B in a 2D plane and I know the ratio of the distance between A to C and B to C, but not the actual distances. How do I find the equation for the curve that represents all the possible coordinates of point C?