Square, diamond, square, diamond

JavaScript (ES6), 294 288 287 284 256 246 240 238 220 bytes

My first golf on this site. Pass input string to function f, e.g. f('codegolf')

f=s=>{N=n=>(2<<n/2+.5)-3-n%2
D=N(l=s.length)
for(a=[],i=S=D*2+1;i--;)a[i]=a[S+~i]=Array(S).fill` `
for(;l--;)for(o=n=N(l+1),I=0;I<=n;I++,o-=~l&1)a[y=D+I][x=D+o]=a[x][y]=a[y][D-o]=a[x][D-I]=s[l]
return a.map(r=>r.join``)}

-6 bytes thanks to @Sunny Pun: Remove parentheses when passing template strings.

-2 bytes thanks to @ETHproductions: Change S-i-1 to S+~i, l%2||o-- to o-=~l&1.

-18 bytes per suggestions of @Sunny Pun, @edc65: Remove prompt() and console.log() in favor of function format, don't .join() final array of strings


Haskell, 138 137 136 bytes

q 1=0
q x=(mod x 2+1)*(q(x-1)+1)
f x|m<-q$length x,n<-abs<$>[-m..m]=[do j<-n;max" "[c|(k,c)<-zip[1..]x,cycle[max i j,i+j]!!k==q k]|i<-n]

Defines a function f which returns the result as a list of lines

-1 byte thanks to @Lynn


C++ - 373 366 362 359 bytes

-1 by @TuukkaX, -6 by @Kevin Cruijssen, -4 by imports, -3 by @Baum mit Augen

#import<string>
#import<vector>
#define A(x) abs(x-r)
using S=std::string;using V=std::vector<S>;int R(int n){return n?(n%2)?R(n-1)+1:2*R(n-1)+2:0;}V f(S w){int l=w.size(),r=R(l-1),s=r*2+1,i,j,k;V x(s);for(i=0;i<s;++i){x[i]=S(s,46);for(j=0;j<s;++j)for(k=0;k<l;++k){if(A(i)<=R(k)&A(j)<=R(k)&k%2?A(i)==R(k)|A(j)==R(k):(A(i)+A(j)==R(k)))x[i][j]=w[k];}}return x;}

http://ideone.com/5y54mx

Note: This solution uses the dot ('.') as "space" character to make the empty spaces more visible. To use a space instead, one has to change S(s,46) to S(s,32). The score remains the same.

Ungolfed:

#import<string>
#import<vector>

#define A(x) abs(x-r) //r will be the center coordinate

using S=std::string;
using V=std::vector<S>;

int R(int n){ //recursive function returning the radius of a square/diamond
    return n?  //if(n!=0)
        (n%2)? //if(n%2 != 0)
            R(n-1)+1 //square -> just increase radius by 1
        :
            2*R(n-1)+2 //diamond -> radius doubles + 2
    :
        0 //n==0 -> end of recursion
    ;
}

V f(S w){ //function taking a string and returning a vector<string>
    int l=w.size(),r=R(l-1),s=r*2+1,i,j,k;  //r is radius (==center coord), s is size
    V x(s);  //vector<string>
    for(i=0;i<s;++i){  //loop over vector
        x[i]=S(s,46); //initialize string with dots. use 32 for spaces
        for(j=0;j<s;++j)
            for(k=0;k<l;++k){ //loop over word
                if(
                    A(i)<=R(k) //check bounds
                    &
                    A(j)<=R(k)
                    &
                    k%2?A(i)==R(k)|A(j)==R(k):(A(i)+A(j)==R(k))
                    //for square: check if distance to center of one coordinate = R
                    //for diamond: check if sum of distances = R
                )
                    x[i][j]=w[k]; //if any is true, replace default char
            }
    }

    return x;
}

Try ungolfed online

How to use:

include<iostream>

void printSquare(std::string word){
    auto result = f(word);
    for(auto& s:result)
        std::cout << s << std::endl;
    std::cout << std::endl << std::endl;
}

int main() {
    printSquare("a");
    printSquare("ab");
    printSquare("cat");
    printSquare("cats");
    printSquare("meow");
    printSquare("meows");
    printSquare("codegolf");
    return 0;
}

Output:

a


bbb
bab
bbb


....t....
...t.t...
..t...t..
.t.aaa.t.
t..aca..t
.t.aaa.t.
..t...t..
...t.t...
....t....


sssssssssss
s....t....s
s...t.t...s
s..t...t..s
s.t.aaa.t.s
st..aca..ts
s.t.aaa.t.s
s..t...t..s
s...t.t...s
s....t....s
sssssssssss


wwwwwwwwwww
w....o....w
w...o.o...w
w..o...o..w
w.o.eee.o.w
wo..eme..ow
w.o.eee.o.w
w..o...o..w
w...o.o...w
w....o....w
wwwwwwwwwww


............s............
...........s.s...........
..........s...s..........
.........s.....s.........
........s.......s........
.......s.........s.......
......s...........s......
.....s.wwwwwwwwwww.s.....
....s..w....o....w..s....
...s...w...o.o...w...s...
..s....w..o...o..w....s..
.s.....w.o.eee.o.w.....s.
s......wo..eme..ow......s
.s.....w.o.eee.o.w.....s.
..s....w..o...o..w....s..
...s...w...o.o...w...s...
....s..w....o....w..s....
.....s.wwwwwwwwwww.s.....
......s...........s......
.......s.........s.......
........s.......s........
.........s.....s.........
..........s...s..........
...........s.s...........
............s............


fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
f............................l............................f
f...........................l.l...........................f
f..........................l...l..........................f
f.........................l.....l.........................f
f........................l.......l........................f
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f.............l.ooooooooooooooooooooooooooo.l.............f
f............l..o............g............o..l............f
f...........l...o...........g.g...........o...l...........f
f..........l....o..........g...g..........o....l..........f
f.........l.....o.........g.....g.........o.....l.........f
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f.......l.......o.......g.........g.......o.......l.......f
f......l........o......g...........g......o........l......f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f....l..........o....g..e....d....e..g....o..........l....f
f...l...........o...g...e...d.d...e...g...o...........l...f
f..l............o..g....e..d...d..e....g..o............l..f
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
fl..............og......ed..oco..de......go..............lf
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
f..l............o..g....e..d...d..e....g..o............l..f
f...l...........o...g...e...d.d...e...g...o...........l...f
f....l..........o....g..e....d....e..g....o..........l....f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f......l........o......g...........g......o........l......f
f.......l.......o.......g.........g.......o.......l.......f
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f.............l.ooooooooooooooooooooooooooo.l.............f
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f........................l.......l........................f
f.........................l.....l.........................f
f..........................l...l..........................f
f...........................l.l...........................f
f............................l............................f
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff


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