From dd08196801f65825c20be34eab9397e1905eb97d Mon Sep 17 00:00:00 2001 From: Revar Desmera Date: Fri, 28 Apr 2023 18:39:26 -0700 Subject: [PATCH] Synopses, etc for trigonometry.scad --- trigonometry.scad | 57 ++++++++++++++++++++++++++++++++++------------- 1 file changed, 42 insertions(+), 15 deletions(-) diff --git a/trigonometry.scad b/trigonometry.scad index 59e99e55..d872f350 100644 --- a/trigonometry.scad +++ b/trigonometry.scad @@ -15,10 +15,12 @@ // Function: law_of_cosines() +// Synopsis: Applies the Law of Cosines for an arbitrary triangle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: law_of_sines() // Usage: // C = law_of_cosines(a, b, c); // c = law_of_cosines(a, b, C=); -// Topics: Geometry, Trigonometry, Triangles // Description: // Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the // angle in degrees for the corner opposite of the third side. Given two side lengths, and the @@ -41,7 +43,6 @@ // c = The length of the third side. // --- // C = The angle in degrees of the corner opposite of the third side. -// See Also: law_of_sines() function law_of_cosines(a, b, c, C) = // Triangle Law of Cosines: // c^2 = a^2 + b^2 - 2*a*b*cos(C) @@ -51,10 +52,12 @@ function law_of_cosines(a, b, c, C) = // Function: law_of_sines() +// Synopsis: Applies the Law of Sines for an arbitrary triangle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: law_of_cosines() // Usage: // B = law_of_sines(a, A, b); // b = law_of_sines(a, A, B=); -// Topics: Geometry, Trigonometry, Triangles // Description: // Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the // angle between them, returns the angle of the corner opposite of the second side. Given a side @@ -78,7 +81,6 @@ function law_of_cosines(a, b, c, C) = // b = The length of the second side. // --- // B = The angle in degrees of the corner opposite of the second side. -// See Also: law_of_cosines() function law_of_sines(a, A, b, B) = // Triangle Law of Sines: // a/sin(A) = b/sin(B) = c/sin(C) @@ -117,10 +119,12 @@ function law_of_sines(a, A, b, B) = // Function: hyp_opp_to_adj() // Alias: opp_hyp_to_adj() +// Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // adj = hyp_opp_to_adj(hyp,opp); // adj = opp_hyp_to_adj(opp,hyp); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length // of the adjacent side. @@ -139,10 +143,12 @@ function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp); // Function: hyp_ang_to_adj() // Alias: ang_hyp_to_adj() +// Synopsis: Returns the adjacent side length from the length of the hypotenuse and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // adj = hyp_ang_to_adj(hyp,ang); // adj = ang_hyp_to_adj(ang,hyp); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the length of the hypotenuse and the angle of the primary corner of a right triangle, // returns the length of the adjacent side. @@ -161,10 +167,12 @@ function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang); // Function: opp_ang_to_adj() // Alias: ang_opp_to_adj() +// Synopsis: Returns the adjacent side length from the length of the opposite side and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // adj = opp_ang_to_adj(opp,ang); // adj = ang_opp_to_adj(ang,opp); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the angle of the primary corner of a right triangle, and the length of the side opposite of it, // returns the length of the adjacent side. @@ -183,10 +191,12 @@ function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang); // Function: hyp_adj_to_opp() // Alias: adj_hyp_to_opp() +// Synopsis: Returns the opposite side length from the lengths of the hypotenuse and the adjacent side. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // opp = hyp_adj_to_opp(hyp,adj); // opp = adj_hyp_to_opp(adj,hyp); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the length of the hypotenuse and the adjacent side, returns the length of the opposite side. // Arguments: @@ -204,10 +214,12 @@ function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj); // Function: hyp_ang_to_opp() // Alias: ang_hyp_to_opp() +// Synopsis: Returns the opposite side length from the length of the hypotenuse and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // opp = hyp_ang_to_opp(hyp,ang); // opp = ang_hyp_to_opp(ang,hyp); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the length of the hypotenuse of a right triangle, and the angle of the corner, returns the length of the opposite side. // Arguments: @@ -225,10 +237,12 @@ function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang); // Function: adj_ang_to_opp() // Alias: ang_adj_to_opp() +// Synopsis: Returns the opposite side length from the length of the adjacent side and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // opp = adj_ang_to_opp(adj,ang); // opp = ang_adj_to_opp(ang,adj); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the length of the adjacent side of a right triangle, and the angle of the corner, returns the length of the opposite side. // Arguments: @@ -246,10 +260,12 @@ function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang); // Function: adj_opp_to_hyp() // Alias: opp_adj_to_hyp() +// Synopsis: Returns the hypotenuse length from the lengths of the adjacent and opposite sides. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // hyp = adj_opp_to_hyp(adj,opp); // hyp = opp_adj_to_hyp(opp,adj); -// Topics: Geometry, Trigonometry, Triangles // Description: // Given the length of the adjacent and opposite sides of a right triangle, returns the length of the hypotenuse. // Arguments: @@ -267,10 +283,12 @@ function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp); // Function: adj_ang_to_hyp() // Alias: ang_adj_to_hyp() +// Synopsis: Returns the hypotenuse length from the length of the adjacent and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // hyp = adj_ang_to_hyp(adj,ang); // hyp = ang_adj_to_hyp(ang,adj); -// Topics: Geometry, Trigonometry, Triangles // Description: // For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse. // Arguments: @@ -288,10 +306,12 @@ function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang); // Function: opp_ang_to_hyp() // Alias: ang_opp_to_hyp() +// Synopsis: Returns the hypotenuse length from the length of the opposite side and the angle. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // hyp = opp_ang_to_hyp(opp,ang); // hyp = ang_opp_to_hyp(ang,opp); -// Topics: Geometry, Trigonometry, Triangles // Description: // For a right triangle, given the length of the opposite side, and the corner angle, returns the length of the hypotenuse. // Arguments: @@ -309,6 +329,9 @@ function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang); // Function: hyp_adj_to_ang() // Alias: adj_hyp_to_ang() +// Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // ang = hyp_adj_to_ang(hyp,adj); // ang = adj_hyp_to_ang(adj,hyp); @@ -329,10 +352,12 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj); // Function: hyp_opp_to_ang() // Alias: opp_hyp_to_ang() +// Synopsis: Returns the angle from the lengths of the hypotenuse and the opposite side. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // ang = hyp_opp_to_ang(hyp,opp); // ang = opp_hyp_to_ang(opp,hyp); -// Topics: Geometry, Trigonometry, Triangles // Description: // For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the corner. // Arguments: @@ -350,10 +375,12 @@ function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp); // Function: adj_opp_to_ang() // Alias: opp_adj_to_ang() +// Synopsis: Returns the angle from the lengths of the adjacent and opposite sides. +// Topics: Geometry, Trigonometry, Triangles +// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp() // Usage: // ang = adj_opp_to_ang(adj,opp); // ang = opp_adj_to_ang(opp,adj); -// Topics: Geometry, Trigonometry, Triangles // Description: // For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner. // Arguments: