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--- new:math [2018/02/18 18:44] – korshun
+++ new:math [2018/02/21 13:11] – korshun
@@ Line 23: / Line 23: @@
   * ''num cmp(num a, num b)'' -- returns 1 if A is greater than B, -1 if lesser, 0 if they are equal.
-==== Other useful functions ====
+==== Other functions ====
-  * ''num mod(num x, num period)'' -- just like ''x % period'', but performs "true" modulo division, without negative results or mirrorings.
+  * ''fixed IntDiv(int x, int y)'' -- divides two integers and returns fixed-point result. Supports any pair of integers whose ratio is less than 32767.
+  * ''fixed AngleDiff(fixed a, fixed b)'' -- returns the shortest signed rotation angle needed to go from angle A to angle B. Result is always in [-0.5, 0.5]. Both A and B may be outside [0.0, 1.0].
+  * ''num gcf(num a, num b)'' -- returns the greatest common factor of two numbers.
+  * ''fixed fract(fixed x)'' -- returns the fractional part of X. For example, ''fract(12.345)'' returns ''0.345''. ''fract(-1234.56789) == 0.56789''.
-Example of practical use of ''mod'' that wouldn't work with ''%'':
-<code>
+==== Powers ====
-int NUM_MENU_ITEMS = 10;
-int selected_item = 0;
-if (KeyPressed(BT_FORWARD))
+  * ''num ipow(num x, int power)'' -- returns x^power. Supports int and fixed X, but only integer powers. Uses a multiplication loop.
-    selected_item--;
+  * ''fixed fpow(fixed x, fixed power)'' -- returns x^power. Supports only fixed-point powers and fixed-point X. Uses multiplication loops.
-if (KeyPressed(BT_BACK))
-    selected_item++;
-// wrap around
-selected_item = mod(selected_item, NUM_MENU_ITEMS);
-</code>
-==== Bit math ====
-  * ''int npo2(int x)'' -- returns the lowest power of 2 greater or equal to X.
-  * ''int bitlog2(int x)'' -- returns the index of the highest used bit, aka integer binary logarithm. Useful to convert flags like ''1<<8 = 256'' back into ''8''.
 ==== Trigonometry ====
@@ Line 65: / Line 55: @@
 Since some functions need to return a vector or a pair of angles, they use the ACSUtils [[multiple return values]] convention.
+<note important>ZDoom [[zdoom>GetActorPitch]] returns actor pitch with the wrong sign (multiplied by -1). Make sure to fix the sign before using actor pitch in the below vector functions.</note>
 Functions returning one value:
   * ''fixed VectorLength3D(fixed x, fixed y, fixed z)'' -- a 3D version of [[zdoom>VectorLength]]. Shorthand for ''VectorLength(z, VectorLength(x, y))''.
-  * ''fixed SqVectorLength(fixed x, fixed y)'' -- squared length of 2D vector. May be faster for length comparisons.
+  * ''fixed SqVectorLength(fixed x, fixed y)'' -- squared length of 2D vector.
   * ''fixed SqVectorLength3D(fixed x, fixed y, fixed z)'' -- squared length of 3D vector.
   * ''fixed dot2(fixed x1, fixed y1, fixed x2, fixed y2)'' -- dot product of two 2D vectors.
@@ Line 79: / Line 71: @@
   * ''fixed, fixed VectorToAngles(fixed x, fixed y, fixed z)'' -- converts vector to a pair of angles (angle and pitch)
   * ''fixed, fixed RotateVector(fixed x, fixed y, fixed angle)'' -- returns vector rotated by angle
-  * ''fixed, fixed RotateVectorSC(fixed x, fixed y, fixed sin, fixed cos)'' -- returns vector rotated by sin and cos of some angle (aka rotation vector). This is useful if you already have the sine and cosine of the rotation angle.
+  * ''fixed, fixed RotateVectorCS(fixed x, fixed y, fixed rx, fixed ry)'' -- returns vector rotated by another vector's angle. Result is multipled by the second vector's length. If the second vector is normalized, it's a (cos(angle), sin(angle)) vector of rotation angle.
   * ''fixed, fixed RotatePoint(fixed x, fixed y, fixed originX, fixed originY, fixed angle)'' -- returns 2D point rotated by angle around the origin.
@@ Line 87: / Line 79: @@
   * ''fixed, fixed, fixed AnglesToVector(fixed angle, fixed pitch)'' -- converts a pair of angles to a vector of length 1.
-<note important>ZDoom [[zdoom>GetActorPitch]] returns actor pitch with the wrong sign (multiplied by -1). Make sure to fix the sign before using actor pitch in the above vector functions.</note>
+==== Other useful functions ====
+=== mod ===
+''num mod(num x, num period)'' -- just like ''x % period'', but performs "true" modulo division, without negative results or mirrorings. It's as if you began at 0 in space [0, period) with wraparound, and moved X steps to the right.
+Example of practical use of ''mod'' that wouldn't work with ''%'':
+<code>
+int NUM_MENU_ITEMS = 10;
+int selected_item = 0;
+if (KeyPressed(BT_FORWARD))
+    selected_item--;
+if (KeyPressed(BT_BACK))
+    selected_item++;
+// wrap around
+selected_item = mod(selected_item, NUM_MENU_ITEMS);
+</code>
+=== lerp ===
+''fixed lerp(fixed a, fixed b, fixed alpha)''
+Performs [[wp>Linear interpolation|linear interpolation]] (or extrapolation) between two numbers and returns the result.
+Simple animation of movement between two points:
+<code>
+for (int time = 0; time < 1.0; time += 0.05)
+{
+    int x = lerp(x1, x2, time);
+    int y = lerp(y1, y2, time);
+    DrawSomething(x, y);
+    Delay(1);
+}
+</code>

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