(* vector3.sml * * COPYRIGHT (c) 1993, AT&T Bell Laboratories. * * 3 dimensional vector arithmetic. *) structure Vector3 : VECTOR = struct type 'a vec = {x : 'a, y : 'a, z : 'a} type realvec = real vec val dim = 3 fun tabulate f = {x = f 0, y = f 1, z = f 2} val zerov = {x = 0.0, y = 0.0, z = 0.0} fun equal({x, y, z}, {x=x1, y=y1, z=z1}) = Real.==(x, x1) andalso Real.==(y, y1) andalso Real.==(z, z1) fun addv ({x=x1, y=y1, z=z1} : realvec, {x=x2, y=y2, z=z2}) = {x=x1+x2, y=y1+y2, z=z1+z2} fun subv ({x=x1, y=y1, z=z1} : realvec, {x=x2, y=y2, z=z2}) = {x=x1-x2, y=y1-y2, z=z1-z2} fun dotvp ({x=x1, y=y1, z=z1} : realvec, {x=x2, y=y2, z=z2}) = x1*x2 + y1*y2 + z1*z2 fun crossvp ({x=x1, y=y1, z=z1} : realvec, {x=x2, y=y2, z=z2}) = {x = y1*z2 - z1*y2, y = x1*z2 - z1*x2, z = x1*y2 - y1*x2} fun addvs ({x, y, z} : realvec, s) = {x=x+s, y=y+s, z=z+s} fun mulvs ({x, y, z} : realvec, s) = {x=x*s, y=y*s, z=z*s} fun divvs ({x, y, z} : realvec, s) = {x=x/s, y=y/s, z=z/s} fun mapv f {x, y, z} = {x = f x, y = f y, z = f z} fun map3v f ({x=x1, y=y1, z=z1}, {x=x2, y=y2, z=z2}, {x=x3, y=y3, z=z3}) = {x = f(x1, x2, x3), y = f(y1, y2, y3), z = f(z1, z2, z3)} fun foldv f {x, y, z} init = f(z, f(y, f(x, init))) fun format {lp, rp, sep, cvt} {x, y, z} = String.concat[ lp, cvt x, sep, cvt y, sep, cvt z, rp ] fun explode {x, y, z} = [x, y, z] fun implode [x, y, z] = {x=x, y=y, z=z} | implode _ = raise Fail "implode: bad dimension" type matrix = { m00 : real, m01 : real, m02 : real, m10 : real, m11 : real, m12 : real, m20 : real, m21 : real, m22 : real } val zerom = { m00 = 0.0, m01 = 0.0, m02 = 0.0, m10 = 0.0, m11 = 0.0, m12 = 0.0, m20 = 0.0, m21 = 0.0, m22 = 0.0 } fun addm (a : matrix, b : matrix) = { m00=(#m00 a + #m00 b), m01=(#m01 a + #m01 b), m02=(#m02 a + #m02 b), m10=(#m10 a + #m10 b), m11=(#m11 a + #m11 b), m12=(#m12 a + #m12 b), m20=(#m20 a + #m20 b), m21=(#m21 a + #m21 b), m22=(#m22 a + #m22 b) } fun outvp ({x=a0, y=a1, z=a2} : realvec, {x=b0, y=b1, z=b2}) = { m00=(a0*b0), m01=(a0*b1), m02=(a0*b2), m10=(a1*b0), m11=(a1*b1), m12=(a1*b2), m20=(a2*b0), m21=(a2*b1), m22=(a2*b2) } end (* VectMath *)
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The output has ended thus: b0), m11=(a1*b1), m12=(a1*b2), m20=(a2*b0), m21=(a2*b1), m22=(a2*b2) } end (* VectMath *)