diff --git a/dist/dist.toml b/dist/dist.toml
index 55cc77d..cf9d505 100644
--- a/dist/dist.toml
+++ b/dist/dist.toml
@@ -61,6 +61,17 @@ test_cases = [
 	{ n = 6, a = -1, b = 1, expected = [-1, -0.73205080756887729, -0.26794919243112271, 0.26794919243112271, 0.73205080756887729, 1] },
 ]
 
+[chebyshev_augmented]
+test_cases = [
+	{ n = 0, a = -1, b = 1, expected = [] },
+	{ n = 1, a = -1, b = 1, expected = [0] },
+	{ n = 2, a = -1, b = 1, expected = [-1, 1] },
+	{ n = 3, a = -1, b = 1, expected = [-1, 0, 1] },
+	{ n = 4, a = -1, b = 1, expected = [-1, -0.70710678118654752, 0.70710678118654752, 1] },
+	{ n = 5, a = -1, b = 1, expected = [-1, -0.86602540378443865, 0, 0.86602540378443865, 1] },
+	{ n = 6, a = -1, b = 1, expected = [-1, -0.92387953251128676, -0.38268343236508977, 0.38268343236508977, 0.92387953251128676, 1] },
+]
+
 [chebyshev_2]
 test_cases = [
 	{ n = 0, a = -1, b = 1, expected = [] },
@@ -200,6 +211,59 @@ test_cases = [
 	{ n = 6, a = -1, b = 1, ratio=10, expected = [-1, -0.99539432839813447, -0.93721714482639173, 0.93721714482639173, 0.99539432839813447, 1] },
 ]
 
+[chebyshev_ellipse_augmented]
+test_cases = [
+	{ n = 0, a = -1, b = 1, ratio=0.1, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=0.25, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=0.5, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=1, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=2, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=4, expected = [] },
+	{ n = 0, a = -1, b = 1, ratio=10, expected = [] },
+	{ n = 1, a = -1, b = 1, ratio=0.1, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=0.25, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=0.5, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=1, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=2, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=4, expected = [0] },
+	{ n = 1, a = -1, b = 1, ratio=10, expected = [0] },
+	{ n = 2, a = -1, b = 1, ratio=0.1, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=0.25, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=0.5, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=1, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=2, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=4, expected = [-1, 1] },
+	{ n = 2, a = -1, b = 1, ratio=10, expected = [-1, 1] },
+	{ n = 3, a = -1, b = 1, ratio=0.1, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=0.25, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=0.5, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=1, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=2, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=4, expected = [-1, 0, 1] },
+	{ n = 3, a = -1, b = 1, ratio=10, expected = [-1, 0, 1] },
+	{ n = 4, a = -1, b = 1, ratio=0.1, expected = [-1, -0.099503719020998914, 0.099503719020998914, 1] },
+	{ n = 4, a = -1, b = 1, ratio=0.25, expected = [-1, -0.24253562503633297, 0.24253562503633297, 1] },
+	{ n = 4, a = -1, b = 1, ratio=0.5, expected = [-1, -0.44721359549995794, 0.44721359549995794, 1] },
+	{ n = 4, a = -1, b = 1, ratio=1, expected = [-1, -0.70710678118654752, 0.70710678118654752, 1] },
+	{ n = 4, a = -1, b = 1, ratio=2, expected = [-1, -0.89442719099991588, 0.89442719099991588, 1] },
+	{ n = 4, a = -1, b = 1, ratio=4, expected = [-1, -0.97014250014533189, 0.97014250014533189, 1] },
+	{ n = 4, a = -1, b = 1, ratio=10, expected = [-1, -0.99503719020998914, 0.99503719020998914, 1] },
+	{ n = 5, a = -1, b = 1, ratio=0.1, expected = [-1, -0.17066403719657229, 0, 0.17066403719657229, 1] },
+	{ n = 5, a = -1, b = 1, ratio=0.25, expected = [-1, -0.39735970711951314, 0, 0.39735970711951314, 1] },
+	{ n = 5, a = -1, b = 1, ratio=0.5, expected = [-1, -0.65465367070797714, 0, 0.65465367070797714, 1] },
+	{ n = 5, a = -1, b = 1, ratio=1, expected = [-1, -0.86602540378443865, 0, 0.86602540378443865, 1] },
+	{ n = 5, a = -1, b = 1, ratio=2, expected = [-1, -0.9607689228305228, 0, 0.9607689228305228, 1] },
+	{ n = 5, a = -1, b = 1, ratio=4, expected = [-1, -0.98974331861078702, 0, 0.98974331861078702, 1] },
+	{ n = 5, a = -1, b = 1, ratio=10, expected = [-1, -0.99833748845958268, 0, 0.99833748845958268, 1] },
+	{ n = 6, a = -1, b = 1, ratio=0.1, expected = [-1, -0.23467915435260521, -0.041385867991006554, 0.041385867991006554, 0.23467915435260521, 1] },
+	{ n = 6, a = -1, b = 1, ratio=0.25, expected = [-1, -0.51673093692781504, -0.10300259910443524, 0.10300259910443524, 0.51673093692781504, 1] },
+	{ n = 6, a = -1, b = 1, ratio=0.5, expected = [-1, -0.77007615237912863, -0.20280301033360352, 0.20280301033360352, 0.77007615237912863, 1] },
+	{ n = 6, a = -1, b = 1, ratio=1, expected = [-1, -0.92387953251128676, -0.38268343236508977, 0.38268343236508977, 0.92387953251128676, 1] },
+	{ n = 6, a = -1, b = 1, ratio=2, expected = [-1, -0.97921955607495314, -0.63795197275105049, 0.63795197275105049, 0.97921955607495314, 1] },
+	{ n = 6, a = -1, b = 1, ratio=4, expected = [-1, -0.99468108687042552, -0.85614784869302944, 0.85614784869302944, 0.99468108687042552, 1] },
+	{ n = 6, a = -1, b = 1, ratio=10, expected = [-1, -0.99914323794470579, -0.97207288539098039, 0.97207288539098039, 0.99914323794470579, 1] },
+]
+
 [chebyshev_ellipse_2]
 test_cases = [
 	{ n = 0, a = -1, b = 1, ratio=0.1, expected = [] },
diff --git a/dist/generate.py b/dist/generate.py
index 73875b3..12072b6 100755
--- a/dist/generate.py
+++ b/dist/generate.py
@@ -57,6 +57,14 @@ def chebyshev(n):
 	return [-mp.cos((2*k - 1) * mp.pi / (2*n)) for k in range(1, n + 1)]
 
 
+def chebyshev_stretched(n):
+	return stretched(chebyshev(n))
+
+
+def chebyshev_augmented(n):
+	return [] if n == 0 else [0] if n == 1 else [-1] + chebyshev(n - 2) + [1]
+
+
 def chebyshev_2(n):
 	return [mp.sin(mp.pi / 2 * x) for x in uniform(n)]
 
@@ -69,10 +77,6 @@ def chebyshev_4(n):
 	return [mp.cos(((2*n - 2 - 2*k) * mp.pi) / (2*n - 1)) for k in range(n)]
 
 
-def chebyshev_stretched(n):
-	return stretched(chebyshev(n))
-
-
 def chebyshev_ellipse(n, ratio):
 	return [mp.sign(2*k+1 - n) / mp.sqrt(1 + (mp.tan(mp.pi * (2*mp.mpf(k) + 1) / (2*n)) / ratio) ** 2) for k in range(n)]
 
@@ -81,6 +85,10 @@ def chebyshev_ellipse_stretched(n, ratio):
 	return stretched(chebyshev_ellipse(n, ratio))
 
 
+def chebyshev_ellipse_augmented(n, ratio):
+	return [] if n == 0 else [0] if n == 1 else [-1] + chebyshev_ellipse(n - 2, ratio) + [1]
+
+
 def chebyshev_ellipse_2(n, ratio):
 	return [0] if n == 1 else [mp.sign(2*k+1 - n) / mp.sqrt(1 + (mp.tan(mp.pi * mp.mpf(k) / (n-1)) / ratio) ** 2) for k in range(n)]
 
@@ -112,8 +120,8 @@ def erf_stretched(n, steepness):
 def generate_test_cases():
 	mapping_intervals_section = 'mapping_intervals = [\n' + '\n'.join([f'\t[{i[0]}, {i[1]}],' for i in mapping_intervals]) + '\n]'
 
-	functions = [uniform, quadratic, cubic, chebyshev, chebyshev_stretched, chebyshev_2, chebyshev_3, chebyshev_4,
-				chebyshev_ellipse, chebyshev_ellipse_stretched, chebyshev_ellipse_2, chebyshev_ellipse_3, chebyshev_ellipse_4,
+	functions = [uniform, quadratic, cubic, chebyshev, chebyshev_stretched, chebyshev_augmented, chebyshev_2, chebyshev_3, chebyshev_4,
+				chebyshev_ellipse, chebyshev_ellipse_stretched, chebyshev_ellipse_augmented, chebyshev_ellipse_2, chebyshev_ellipse_3, chebyshev_ellipse_4,
 				logistic, logistic_stretched, erf, erf_stretched]
 	sections = []