Remove useless exponentiation in fractals generators by multiplying t…

…he value in the loop (as suggested for fbm in #299). Fixed calc_scale_factor in fbm constructor.

examples/README.md

@@ -438,14 +438,14 @@ cargo run --example "super_simplex" --features="images"
 ```
 cargo run --example "terrace" --features="images"
 ```
-![terrace_inverted.png]
-
-*terrace_inverted.png*
-
 ![terrace.png]
 
 *terrace.png*
 
+![terrace_inverted.png]
+
+*terrace_inverted.png*
+
 
 ## [texturegranite](/examples/texturegranite.rs)
 
@@ -765,10 +765,10 @@ cargo run --example "worley" --features="images"
 
 [super_simplex 3d.png]: /images/examples/super_simplex%203d.png
 
-[terrace_inverted.png]: /images/examples/terrace_inverted.png
-
 [terrace.png]: /images/examples/terrace.png
 
+[terrace_inverted.png]: /images/examples/terrace_inverted.png
+
 [texture_granite_planar.png]: /images/examples/texture_granite_planar.png
 
 [texture_granite_seamless.png]: /images/examples/texture_granite_seamless.png

src/noise_fns/generators/fractals/basicmulti.rs

@@ -166,6 +166,7 @@ where
 
         // if only 1 octave of noise, then return result unchanged, otherwise process another octave
         if self.octaves > 1 {
+            let mut attenuation = self.persistence;
             // Spectral construction inner loop, where the fractal is built.
             for x in 1..self.octaves {
                 // Raise the spatial frequency.
@@ -175,7 +176,10 @@ where
                 let mut signal = self.sources[x].get(point.into_array());
 
                 // Scale the amplitude appropriately for this frequency.
-                signal *= self.persistence.powi(x as i32);
+                signal *= attenuation;
+
+                // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+                attenuation *= self.persistence;
 
                 // Scale the signal by the current 'altitude' of the function.
                 signal *= result;
@@ -204,6 +208,7 @@ where
 
         // if only 1 octave of noise, then return result unchanged, otherwise process another octave
         if self.octaves > 1 {
+            let mut attenuation = self.persistence;
             // Spectral construction inner loop, where the fractal is built.
             for x in 1..self.octaves {
                 // Raise the spatial frequency.
@@ -213,7 +218,10 @@ where
                 let mut signal = self.sources[x].get(point.into_array());
 
                 // Scale the amplitude appropriately for this frequency.
-                signal *= self.persistence.powi(x as i32);
+                signal *= attenuation;
+
+                // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+                attenuation *= self.persistence;
 
                 // Scale the signal by the current 'altitude' of the function.
                 signal *= result;
@@ -242,6 +250,7 @@ where
 
         // if only 1 octave of noise, then return result unchanged, otherwise process another octave
         if self.octaves > 1 {
+            let mut attenuation = self.persistence;
             // Spectral construction inner loop, where the fractal is built.
             for x in 1..self.octaves {
                 // Raise the spatial frequency.
@@ -251,7 +260,10 @@ where
                 let mut signal = self.sources[x].get(point.into_array());
 
                 // Scale the amplitude appropriately for this frequency.
-                signal *= self.persistence.powi(x as i32);
+                signal *= attenuation;
+
+                // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+                attenuation *= self.persistence;
 
                 // Scale the signal by the current 'altitude' of the function.
                 signal *= result;

src/noise_fns/generators/fractals/billow.rs

@@ -158,6 +158,8 @@ where
 
         let mut result = 0.0;
 
+        let mut attenuation = self.persistence;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -169,7 +171,10 @@ where
             signal = scale_shift(signal, 2.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi((x as i32) + 1);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;
@@ -193,6 +198,8 @@ where
 
         let mut result = 0.0;
 
+        let mut attenuation = self.persistence;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -204,7 +211,10 @@ where
             signal = scale_shift(signal, 2.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi((x as i32) + 1);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;
@@ -228,6 +238,8 @@ where
 
         let mut result = 0.0;
 
+        let mut attenuation = self.persistence;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -239,7 +251,10 @@ where
             signal = scale_shift(signal, 2.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi((x as i32) + 1);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;

src/noise_fns/generators/fractals/fbm.rs

@@ -55,10 +55,6 @@ pub struct Fbm<T> {
     scale_factor: f64,
 }
 
-fn calc_scale_factor(persistence: f64, octaves: usize) -> f64 {
-    1.0 - persistence.powi(octaves as i32)
-}
-
 impl<T> Fbm<T>
 where
     T: Default + Seedable,
@@ -78,7 +74,10 @@ where
             lacunarity: Self::DEFAULT_LACUNARITY,
             persistence: Self::DEFAULT_PERSISTENCE,
             sources: super::build_sources(seed, Self::DEFAULT_OCTAVE_COUNT),
-            scale_factor: calc_scale_factor(Self::DEFAULT_PERSISTENCE, Self::DEFAULT_OCTAVE_COUNT),
+            scale_factor: Self::calc_scale_factor(
+                Self::DEFAULT_PERSISTENCE,
+                Self::DEFAULT_OCTAVE_COUNT,
+            ),
         }
     }
 

src/noise_fns/generators/fractals/hybridmulti.rs

@@ -168,6 +168,8 @@ where
     fn get(&self, point: [f64; 2]) -> f64 {
         let mut point = Vector2::from(point);
 
+        let mut attenuation = self.persistence;
+
         // First unscaled octave of function; later octaves are scaled.
         point *= self.frequency;
         let mut result = self.sources[0].get(point.into_array()) * self.persistence;
@@ -185,7 +187,10 @@ where
             let mut signal = self.sources[x].get(point.into_array());
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add it in, weighted by previous octave's noise value.
             result += weight * signal;
@@ -207,6 +212,8 @@ where
     fn get(&self, point: [f64; 3]) -> f64 {
         let mut point = Vector3::from(point);
 
+        let mut attenuation = self.persistence;
+
         // First unscaled octave of function; later octaves are scaled.
         point *= self.frequency;
         let mut result = self.sources[0].get(point.into_array()) * self.persistence;
@@ -224,7 +231,10 @@ where
             let mut signal = self.sources[x].get(point.into_array());
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add it in, weighted by previous octave's noise value.
             result += weight * signal;
@@ -246,6 +256,8 @@ where
     fn get(&self, point: [f64; 4]) -> f64 {
         let mut point = Vector4::from(point);
 
+        let mut attenuation = self.persistence;
+
         // First unscaled octave of function; later octaves are scaled.
         point *= self.frequency;
         let mut result = self.sources[0].get(point.into_array()) * self.persistence;
@@ -263,7 +275,10 @@ where
             let mut signal = self.sources[x].get(point.into_array());
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ (x + 1)
+            attenuation *= self.persistence;
 
             // Add it in, weighted by previous octave's noise value.
             result += weight * signal;

src/noise_fns/generators/fractals/ridgedmulti.rs

@@ -201,6 +201,8 @@ where
         let mut result = 0.0;
         let mut weight = 1.0;
 
+        let mut attenuation = 1.0;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -226,7 +228,10 @@ where
             weight = weight.clamp(0.0, 1.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ x
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;
@@ -260,6 +265,8 @@ where
         let mut result = 0.0;
         let mut weight = 1.0;
 
+        let mut attenuation = 1.0;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -285,7 +292,10 @@ where
             weight = weight.clamp(0.0, 1.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ x
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;
@@ -319,6 +329,8 @@ where
         let mut result = 0.0;
         let mut weight = 1.0;
 
+        let mut attenuation = 1.0;
+
         point *= self.frequency;
 
         for x in 0..self.octaves {
@@ -344,7 +356,10 @@ where
             weight = weight.clamp(0.0, 1.0);
 
             // Scale the amplitude appropriately for this frequency.
-            signal *= self.persistence.powi(x as i32);
+            signal *= attenuation;
+
+            // Increase the attenuation for the next octave, to be equal to persistence ^ x
+            attenuation *= self.persistence;
 
             // Add the signal to the result.
             result += signal;