Solunars by Aldebaran Sidereal Academy

Jim Eshelman wrote: Tue Apr 23, 2024 8:05 am I don't know if Mikestar13 used complicated "shaping" code for angularity, or it's a straight value. This makes a small difference in how the value is calculated.

def minor_angularity_curve(a):
    if a <= 2:
        x = 3 * a / 2
    else:
        x = (a - 2) * 7 + 3
    a = x * 6
    return math.cos(math.radians(a))

Mike V wrote: Mon May 27, 2024 9:39 pm Asc 24°Vi55' - planet 24°Sg23' - 98% strength (32' orb)
RAMC 40°31' - planet RA 308°06' - 65% strength (2°25' orb, if I did the math correctly)
RAMC 167°28' - planet RA 78°41' - 90% strength (1°13' orb? I think?)
Asc 2°Ar41' - planet 4°Cap35' - 77% strength (1°54' orb)

Does this look correct?

Mike V wrote: Thu Jun 06, 2024 12:32 am I'm not sure what the history is on this secondary correction. Should I scrap it?

1. Let's look at the major angle model first: The more complex equations produce an initial value that ranges between -1.0 and +1.0 (the range of the cosine function). We want this displayed, instead, as 0% to 100%. I would do this by adding +1 (so that it ranges from 0.0 to +2.0), divide by 2 (so that it ranges from 0.0 to +1.0), then multiply by 100 (converting units to percents). -- Add 1, divide by 2, multiply by 100 is the same as add 1 and multiply by 50.
2. Except... (I almost forgot this detail): This major angle -1.0 to +1.0 isn't a single cosine curve. It's TWO cosine curves (each of which begins as -1.0 to +1.0). This detail matters because we want to preserve the sinusoidal shape throughout.) This full major angle curve is really one foreground curve centered on each angle and one background curve centered on each cadent cusp. The shape of angularity, then, is not the whole -1 to +1 range of the butt-to-butt dual curves but, rather, the shape of the foreground curve only (or the background curve only). [Mike's larger process of calculating full quadrant major angle scores is beyond the current discussion.]
3. For all angularity, scaling "above 50%" of the foreground curve as foreground, and "under -50%" of the background curve as background gives: Background is below 25%, foreground above 75%, and the rest is middleground. (This is important to know because aspects and angularity need to be treated differently.)
4. For minor angles, the initial value using a 3° orb comes from this logic: 3° orb means 3° either side (6° range of "in orb" centered on 0°00') and then double that amount for the negative cosine range (6° either side = 12° "base" for the curve). The cosine curve needs to rise from -1 to +1 and back down the other side over this 12° range. Therefore, divide the whole 360° circle by 12° to get the 30x multiplier.
5. Repeating in different words to be clear (presuming our default orbs and not worrying for now about the final display scaling): A cosine curve runs from +1 to -1. A major angle curve that reaches 0.0 (50% of the whole range) at 10° covers this full slope in 20°. -- To match this, a minor angle curve that reaches 0.0 (50% of the whole range) at 3° covers this full slope in 6° [on each side].
6. The minor angle curve ranges -1 to +1. Its halfway point (0.0) has to be called 75% in the same way that a 10° major angle orb is called 75%. It gets a little confusing here (in order to preserve the shape of the curve): The full major angle curve includes a second curve "underneath" it giving the first 50%; this doesn't exist in the minor angle curve. So, for the minor angle (running from -1 to +1) we to add 1 (changing it to 0.0 to +2.0), spread this across 50 percentage points (x25 = 0% to 50%), and add 50 (= 50% to 100%). Foreground then begins at half of this, or 75%, just like the major angle curve.
7. ((x +1)x25)+50 = 25x + 75

Here's an example using the minor angle formula we're talking about in this thread - that is,
f(cos(radians(orb_degrees * 30)) + 3) / 4:
Random chart for 2 Jan 1998 0:45am PST

Eris RA: 22*47' (22.78); RAMC 114*41' (114.68); orb = 1.9*

The raw value I get for the minor angle formula is 0.88604, which after rounding in this manner, becomes 94%.

0	0	100.0%
0	30	99.1%
1	0	96.7%
1	30	92.7%
2	0	87.5%
2	30	81.5%
3	0	75.0%
3	30	68.5%
4	0	62.5%
4	30	57.3%
5	0	53.3%
5	30	50.9%
6	0	50.0%