User:McArine/Incense - Revision history

McArine: /* My approach to determining incense coordinates */

2011-03-31T14:39:56Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-03-31T14:37:56Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-03-31T14:16:14Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T18:06:05Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T18:05:05Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T18:04:49Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T18:03:05Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T17:58:43Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T17:58:21Z

My approach to determining incense coordinates

McArine: /* My approach to determining incense coordinates */

2011-02-03T17:57:46Z

My approach to determining incense coordinates

@@ Line 5: / Line 5: @@
 In T4 the formula for calculating incense qualities was found, and we can see that it hasn't changed in T5.<br>
-The current location in simple form:
+The current location in simple form, using only 1 resin:
 *Sx + n*Rx

@@ Line 38: / Line 38: @@
   a² + b² = c²
-Where a is the estimated distance between your (Xn, Yn) and the intersection of the circle and the line.<br>
+Where a is the estimated distance between your (Xn, Yn) and the intersection of the circle and the line(the closest point found in loop 2).<br>
-b is the distance from the intersection to the circle center.<br>
+b is the distance from the intersection to the circle center(the one to be eliminated).<br>
-And c is the distance between the (Xn, Yn) and the circle center.<br>
+And c is the distance between the (Xn, Yn)(from above) and the circle center(Attibute point).<br>
-Now a is depending on the distance between S and R, and also on the intersection, which is also depending on the distance between S and R. (and we need to try all locations between the two maximum quality points.)<br>
+Now a is depending on the distance between S and R, and also on the intersection, which is also depending on the distance between S and R. (and we need to try all locations between the two maximum quality points, loop 1 and loop 2)<br>
 b is the radius of the circle: r.
-c is the radius of the circle, plus the difference in quality from (Xn, Yn) to the center(Dq). And we have a good estimate of this.
+c is the radius of the circle, plus the difference in quality from (Xn, Yn)(the value from our test) to the center(the value we have from loop 3), lets call it Dq.
 So the formula becomes:
@@ Line 57: / Line 57: @@
 And for each n location on the line between R and S, that had the same closest attribute. rn can be calculated, and compared to the others, until the best location is found.<br>
-Using this formula I can calculate a very good location in less than 1 second, with 0.1 accuracy. This would take hours using my first approach.
+The way that quality is calculated is 1000 - Resin - Herb - Rose. Where Resin, Herb and Rose is the distance from the current location in the three planes to the closest Attribute in that plane. So if we're 55 coords from StrClum in Resin, 42 coords from Honey in Herb and 149 from Invigorating in Rose, the quality is 1000 - 55 - 42 - 149 = 754.<br>
 Some notes: this works best when using values that differ by more than 20 from start to max.<br>
 The formula does not figure out if the actual location of A is positive or negative.<br>
-I don't have a minimum requirement for number of locations for calculating using this approach, but I've had good results using 7 points.
+I don't have a minimum requirement for number of locations for calculating using this approach, but I've had good results using 7 points, I've also been able to get good results from 4 points with large differences.

@@ Line 11: / Line 11: @@
 + n
-*Yx + n*Yx
+*Sy + n*Ry
   Yn = ------------
 + n
@@ Line 17: / Line 17: @@
 This is the current location between Startpoint and Resinpoint, where n is the amount of resin added.<br>
 This gives us a string of locations that are dependent upon the Start and Resin points.<br>
-At each of these points we have a quality measure, and an attribute, that indicates to us, how far we are from the closest attribute.<br>
+At each of these points we have a quality measure, and an attribute, that indicates to us, how far we are from that closest attribute.<br>
 As we don't know the location of the Attribute point, we don't know how far away it is, we just know how much closer to, or further away from the point we get, each time we add a deben of resin.<br>
-So that was initially what I used to calculate locations, the difference in quality, between to deben of resin.<br>
+So that was initially what I used to calculate locations, the difference in quality, between two deben of resin.<br>
 And the maths for this gets a bit hairy, I can tell you.
@@ Line 26: / Line 26: @@
 [[Image:IncenseA1.png]]
-And realised that I had a lot of right angle triangles in this image. I didn't know the exact location where the circle intersected the line, because I didn't know the size of the circle. So what's good about this.
+And realised that I had a lot of right angle triangles in this image. I didn't know the exact location where the circle intersected the line, because I didn't know the size of the circle... So what's good about this.
-Well, when you test your resin, you get a lot of data, and from this, you can see between which two points the line is closest. You can also get a good estimate of how large the circle is. By looking at the quality from those two points. And this helps us a lot.<br>
+Well, realizing this you can build a simpler program, that can figure out the distance between Start and Resin points. Can calculate where the Attribute point is closest, at what distance it is from the line between Start and Resin points. And another cool thing, you can get how far from the start attribute, the start point is. And these things helps us a lot.<br>
-Where you previously brute forced through a lot of coordinates, without much accuracy. With this approach you only have to move one coordinate, then the rest can be calculated. Then you just need to estimate the intersection between the circle and the line, and you know got a pythagorean triangle. That you can simply verify the sizes of, by calculating the hypotenuse.
+Where you previously brute forced through a lot of coordinates, without much accuracy. This approach can be done with three loops, in a program. But you don't know any boundaries for those loops.<br>
 The math is like this:<br>

@@ Line 20: / Line 20: @@
 As we don't know the location of the Attribute point, we don't know how far away it is, we just know how much closer to, or further away from the point we get, each time we add a deben of resin.<br>
-So that was initially what I used to calculate locations, the difference in quality, between to deben of resin.
+So that was initially what I used to calculate locations, the difference in quality, between to deben of resin.<br>
 Then one day, I drew something like this:<br>

← Older revision		Revision as of 18:05, 3 February 2011
Line 31:		Line 31:

	The math is like this:<br>		The math is like this:<br>
−
−	~~<math>a^2 + b^2 = c^2</math>~~

	a² + b² = c²		a² + b² = c²

← Older revision		Revision as of 18:04, 3 February 2011
Line 31:		Line 31:

	The math is like this:<br>		The math is like this:<br>
		+
		+	<math>a^2 + b^2 = c^2</math>

	a² + b² = c²		a² + b² = c²

@@ Line 44: / Line 44: @@
 So the formula becomes:
-a² + r² = (Dq + r)²
+ a² + r² = (Dq + r)²
 This can be transformed into
-    a² + Dq²
+     a² + Dq²
-r = --------
+ r = --------
 *Dq