On this day of Valentine s Day, write a heartbeat code in C and confess it!

On February 14, 2024, today is Valentine's Day!

I don't know if you have watched Li Xun's love on the TV series "Ignite Me, Warm You", so I will show you a little here.

How to make a heart beating heart program?

Find the high-numbered cardioid parametric equation:

x = sin^3(θ)

y = (13 * cos(θ)5 * cos(2θ) 3 * cos(3θ) cos(4θ))/ 16

From the above equation, a number of points on the curve can be obtained, which are denoted as the set s

Step 2: Generate points within the curve.

For the internal points, we diffuse s inward so that it conforms to the exponential distribution, and we get s'

Let e m, n] and e e( ).

Inward diffusion of p (x, y) s yields point p' ∈ s':

p' = (x, y) *e

The degree of diffusion depends on the parameters m, n,

For the outer points, we diffuse s outward so that it conforms to a uniform distribution, and we get s''

Let u u [1, 1 + b].

Spread outward to p (x, y) s to get the point p'' ∈ s'':

p'' = (x, y) *u

The degree of diffusion depends on parameter b

The above knowledge foreshadowing can only achieve a static pattern, and in order to achieve an animation effect, it is necessary to add a periodic beating to simulate the process of our heart beating.

Introduce the time parameter t and the periodic function t(t) = sin 2(t) (can be other periodic functions, depending on the effect).

For p s u s'

The degree of periodic scaling is inversely proportional to its distance d from the origin, which can be measured by r d (r is the radius of the cardioid curve).

Add order i to it to increase the effect of distance on the degree of scaling (r d) i

We can get the following function.

d' = d * 1 + a * t(t) *r/d)^i)

Run the program, which runs the test in the Visual C++ 2022 operating environment.

Compiler the program, run.

You can see a heart-shaped beating animation pop up directly.

The program** interception is not complete, you can send a private message if you need it.

Valentine's Day