초록 ▼

A method of evaluating a tetrahedral linear interpolation function utilizes a table preparation process and a linear interpolating process. In the table preparation process, values v and domain points p of the function are related by two tetrahedral interpolation variables denoted as a matrix T and

A method of evaluating a tetrahedral linear interpolation function utilizes a table preparation process and a linear interpolating process. In the table preparation process, values v and domain points p of the function are related by two tetrahedral interpolation variables denoted as a matrix T and a vector t, as follows: v=t+pT. The coordinates of p include n components, and the value v includes m components. The matrix T includes n rows and m columns, as it must to relate p to v. If the value of the function is scalar, t is also a scalar, and T is a vector of n elements. From the coordinates of the (n+1) domain input points and the function values v at these points, the values of variables t and T are computed and stored in a table. The linear interpolation procedure of the invention uses the values tabulated for t and T to calculate an approximation for the components of the function value v at a given p. The function arguments are stored in a first array of n elements denoted as p[i], and the calculated approximations are to be stored in a second array of m elements denoted as v[j]. The approximations for the array v[j] may be calculated according to the following equation: ]EQU1 ]

대표청구항 ▼

[ I claim:] [1.] An arithmetic apparatus for converting an input color signal to an output color signal, said apparatus approximating a value v of a function having a domain input in a first three-dimensional color space and a range output in a second four-dimensional color space, the domain input b

[ I claim:] [1.] An arithmetic apparatus for converting an input color signal to an output color signal, said apparatus approximating a value v of a function having a domain input in a first three-dimensional color space and a range output in a second four-dimensional color space, the domain input being divided into a plurality of rectangular volumes, each said rectangular volume being further subdivided into a plurality of tetrahedra, each said tetrahedron having four vertices, vertices of each of the tetrahedra comprising sample domain input points p, each said sample domain input point p having a set of coordinates in the first color space, the apparatus comprising;an input port to accept from an input device an input signal corresponding to an input image pixel of the input device, said input signal being represented by a set of coordinates for a domain input point P situated within the first three-dimensional color space, the point P having coordinates x, y, and z, such that x represents a first color component in the first three-dimensional color space, y represents a second color component in the first three-dimensional color space, and z represents a third color component in the first three-dimensional color space;a first demultiplexer for separating the domain input point P into a demultiplexed output comprising first, second and third color components;a memory containing a tetrahedral interpolation constants table, said table including:the domain input divided into a plurality of tetrahedral volumes, each tetrahedral volume having four vertices i, each vertex i having vertex coordinates x(i,j) in the first three-dimensional color space and an associated range output value v at the vertex i of v(i,k);a matrix T comprising the inverse of an n.times.n matrix X multiplied by an n.times.m matrix V; wherein matrix X comprises matrix components X(i,j) defined as X(i,j)=x(i+1,j)-x(0,j) for 0.ltoreq.j.ltoreq.n-1 and 0.ltoreq.j.ltoreq.m-1, and wherein matrix V comprises matrix components V(i,k) defined as V(i,k)=v(i+1,k)-v(0,k) for 0.ltoreq.i.ltoreq.n-1 and 0.ltoreq.k.ltoreq.m-1;a vector t comprising vector components t(k) wherein t(k)=v(0,k)-x(0,k)*T for 0.ltoreq.k.ltoreq.m-1;wherein the tetrahedral interpolation constants table is structured to map between each tetrahedra vertex and first, second, and third multiplicative constants that comprise corresponding components of the matrix T, and to also map between each tetrahedra vertex and an additive constant comprising a corresponding component of the vector t, wherein each constant includes first, second, and third color components;a selector coupled to the input port and the memory for selecting the tetrahedron containing the point p; anda signal processor coupled to the memory and to the demultiplexer output for producing an output signal corresponding to an image pixel of an output device and represented by an output signal value v in the second four-dimensional color space, the output signal value v having a first color constituent a, a second color constituted b, a third color constituent c, and a fourth color constituent d; the signal processor including first signal processor associated with the first color component for producing a first color output representative of the first color constituent a, a second signal processor associated with the second color component for producing a second color output representative of the second color constituent b, a third signal processor associated with the third color component for producing a third color output representative of the third color constituent c, and a fourth signal processor for producing a forth color output, representative of the fourth color constituent; each of the first, second, third and fourth signal processor means including:(i) first multiplication means for producing a first product by multiplying the first component of the demultiplexer output by a corresponding component of the first multiplicative constant;(ii) second multiplication means for producing a second product by multiplying the second component of the demultiplexer output by a corresponding component of the second multiplicative constant;(iii) third multiplication means for producing a third product by multiplying the third component of the demultiplexer output by a corresponding component of the third multiplicative constant;(iv) first summing means for producing a first sum by adding the first product to the second product;(v) second summing means for producing a second sum by adding the first sum to the third product;(vi) third summing means for producing a third sum by adding the second sum to a corresponding component of the additive constant; the third sum comprising a color output for the respective color constituent;wherein the set of coordinates for the selected domain input point p is expressed as an 8 bit number having four high order bits and four low order bits, the four high order bits indicating a particular one of said plurality of rectangular volumes which includes the selected domain input point p, the four low order bits indicating a particular one of said plurality of tetrahedral volumes which includes the selected domain input point p; the arithmetic apparatus further including a second demultiplexer, having a second demultiplexer input and a second demultiplexer output, to separate a domain input point p at the second demultiplexer input into four low order bits and four high order bits at the second demultiplexer output, the second demultiplexer input being coupled to the input port, the second demultiplexer output being coupled to the selector, the selector further including:(i) rectangular volume selector responsive to the four high order bits to select the particular one of said plurality of rectangular volumes; and(ii) tetrahedral volume selector responsive to the four low order bits to select the particular one of said plurality of tetrahedral volumes.