## How to describe a circle trajectory on nes?

Discuss technical or other issues relating to programming the Nintendo Entertainment System, Famicom, or compatible systems.

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MartsINY
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### How to describe a circle trajectory on nes?

Simple, I know radius and angle.

I want to obtain X and Y positions

In real life, I would simply use sinus for the first unknown, then pythagore for the second one.

However I don't have a sin function neither a square root function.

I wouldn't want to enter values by hand in an array...

is there a better way?

rainwarrior
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### Re: How to describe a circle trajectory on nes?

A lookup table is effective, but since you've ruled that out...

If you can compromise on the shape a little bit, and would accept a circle-like curve, you might try a second-order approximation by just accelerating something alternately up, right, left, down at a fixed rate. i.e. accelerate right for 1 second, then accelerate down for 1 second... the object should travel in a stable curved path. Controlling the speed and radius specifically is a bit tricky, but it's not too hard to just tweak it until it looks right as an easier method.

* Also your starting velocity has to be 90 degrees rotated from your starting acceleration, or else you might get a diagonal oscillation instead of circular, i.e. if you start by accelerating up, set the initial velocity to full left, etc.

You can also use this kind of thing to seek toward a point, the value you clamp velocity at will determine the radius of the orbit.

You can also use this idea in 2D for a simple up-down sine-like motion (e.g. castlevania medusa).
Last edited by rainwarrior on Thu Dec 28, 2017 11:58 am, edited 1 time in total.

tepples
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### Re: How to describe a circle trajectory on nes?

MartsINY wrote:Simple, I know radius and angle.

I want to obtain X and Y positions
[...]
I wouldn't want to enter values by hand in an array...

is there a better way?
Yes: a Python script to generate the array that you bake into the ROM.

MartsINY
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Joined: Sun Jun 11, 2017 5:39 pm

### Re: How to describe a circle trajectory on nes?

tepples wrote:
MartsINY wrote:Simple, I know radius and angle.

I want to obtain X and Y positions
[...]
I wouldn't want to enter values by hand in an array...

is there a better way?
Yes: a Python script to generate the array that you bake into the ROM.
Is that easy to incorporate the python script? Can you export the assembly and use it somehow?

tepples
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### Re: How to describe a circle trajectory on nes?

A table generator program just needs to write a file full of .byte statements that you .include in your main assembly file. An example of such a table generator for an exponential function is at APU period table. It should be straightforward to adapt it to a sine table.

nesrocks
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### Re: How to describe a circle trajectory on nes?

Isn't that doing exactly what you said you didn't want to do? rainwarrior's solution looks good.

tepples
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### Re: How to describe a circle trajectory on nes?

A table generator avoids the "by hand" in "I wouldn't want to enter values by hand in an array."

MartsINY
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### Re: How to describe a circle trajectory on nes?

nesrocks wrote:Isn't that doing exactly what you said you didn't want to do? rainwarrior's solution looks good.
yeah I though of a table with X and Y this I didn't want.

However a table with sin and cos values would be better.

I will generate one through matlab

thanks!!

tokumaru
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### Re: How to describe a circle trajectory on nes?

MartsINY wrote:However a table with sin and cos values would be better.
But then you need multiplications to do anything useful with those look-up tables. The 6502 isn't particularly good with multiplications, but you can do a handful of them per frame if you really need to. Just something to keep in mind.

MartsINY
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### Re: How to describe a circle trajectory on nes?

tokumaru wrote:
MartsINY wrote:However a table with sin and cos values would be better.
But then you need multiplications to do anything useful with those look-up tables. The 6502 isn't particularly good with multiplications, but you can do a handful of them per frame if you really need to. Just something to keep in mind.
thanks!! actually I'm lucky mega man has a multiplication function!!

psycopathicteen
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### Re: How to describe a circle trajectory on nes?

There is a way to multiplying a sine wave by adding two sine waves. I'm not sure how much precision it would have.

Zutano
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### Re: How to describe a circle trajectory on nes?

If you really want to do it without a lookup table, you could approximate the value using the Taylor series for sin/cos, calculated out to some degree of precision.
https://en.wikipedia.org/wiki/Taylor_se ... _functions

But then you'd need functions for division, exponentiation, and factorial all without lookup tables...
By the time you coded that all up, it would likely use more ROM than just having the original, single lookup table.
http://zutanogames.com/ <-- my dev blog

rainwarrior
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### Re: How to describe a circle trajectory on nes?

Those Taylor series are just one of many ways to compute that stuff, and they're really not a good way to go about it on 6502.

This is a well known set of techniques that's actually designed for this kind of hardware:
https://en.wikipedia.org/wiki/CORDIC
psycopathicteen wrote:There is a way to multiplying a sine wave by adding two sine waves. I'm not sure how much precision it would have.
Yes, it's due to the family of identities that relate multiplication to sum and difference, e.g.:

cos(a) * cos(b) = (cos(a+b) + cos(a-b)) / 2

So if you have a cosine/sine table, you can get the multiplied result with a few sums, a few lookups, and a shift. Each step loses some precision, yes. I've half-written an NES demo experimenting with this concept but I haven't gotten around to finishing it yet.

Though, if you only need one size of circle you don't need any multiplication, just scale your sine table to the size of the circle to begin with. You only need to be multiplying if you are trying to reuse one sine table at various scales.

psycopathicteen
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### Re: How to describe a circle trajectory on nes?

If the sine table goes from -127 to 127, you would need at least 1024 sine table entries for every step.

rainwarrior
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