Make a Surfin' Word

Question

Your goal is to map a piece of text to a sine curve of the form:

a sin ( mx - b )

Where a and m are non-zero rational numbers, b is a rational number, and the calculations are in radians.

It doesn't really matter where the origin of your graph is, as long as you fit all the letters in your output. Also, it must be ASCII art, no graphical output.

You can take the equation input in as a string OR you can have a separate input for each parameter: a, m, and b.

Also

Examples:

Input: "A-well-a", "3sin(x)" or (3,1,0)

Output:

 -w
       a
     
A  e       
      -
    l
     l

Explanation:

The index of the character is the x-value, and each line represents one y-value. So we take 3sin(x) of the appropriate indices and round them to the nearest integer to get our values:

  'A' : 3sin(0) = 0 => (0,0)
  '-' : 3sin(1) = 2.5244 => (1,3)
  'w' : 3sin(2) = 2.7279 => (2,3)
   etc. , to give you the rest of the word.

---

Input: "Everybody's", "3.5sin(x-2)" or (3.5,1,2)

Calculations:

3.5sin(x-2), x = 0,1,2,3,...,10 -3.1815,-2.9435,0,2.9435,3.1815,0.4935,-2.6495,-3.3565,-0.9765,2.2995,3.4615,

Output:

   ry     s
         '

  e  b
        y

Ev    od

---

Input: "heard", "4sin(2x)" or (4,2,0)

4sin(2x) [0-4] = 0,3.636,-3.028,-1.116,3.956,

Output:

 e  d



h
   r

  a

---

Input: "about","-5sin(x+1)" or (-5,1,-1)

-5sin(x+1) [0-4] : -4.205,-4.545,-0.705,3.785,4.795,

Output:

    t
   u




  o


a
 b

---

Input: "the word", "-2.4sin(0.5x-1.2)" or (-2.4,0.5,1.2)

-2.4sin(0.5x-1.2) [0-7] : 2.2368,1.5456,0.4776,-0.7104,-1.7208,-2.3136,-2.3376,-1.7904

Output:

th

  e
    
    word

See also

Answer 1

Dyalog APL, 37 bytes

{⍉↑v⌽¨⍵↑¨⍨v←(-∘1-⌈/)⌊.5+⎕×1○⎕-⍨⎕×⍳≢⍵}

Takes text as right argument, and then prompts for m, b, and a.

Answer 2

Python 2, 190 159 171 bytes

import math
a,b,c,d=input()
q=len(a)
s=""
m=int(abs(b)+.5)
for i in range(2*m*q+q):s+=""if i%q else"\n";s+=a[i%q]if i/q==-int(round(b*math.sin(i%q*c-d)))+m else" "    print s

Example usage:

$ python2 surfin2.py
"about",-5,1,-1

    t
   u




  o


a
 b

This can probably be golfed further, but I can't see how at the moment. I just wanted to see this question get at least one answer. EDIT: Decently golfed once I saw how to do it in one pass. May have extra leading and trailing lines, but such was expressly allowed: "It doesn't really matter where the origin of your graph is, as long as you fit all the letters in your output."