An apparatus for rotating 90 degrees a multivalued source picture image consisting of pieces of picture data a.sub.ij (i =0,1, - - - ,N, j=0,1, - - - , m*N-1) arranged in a matrix of N rows.times.(m gradations*N) columns, comprising:
- picture image storing means for storing a multivalued source picture image consisting of pieces of picture data a.sub.ij (i=0,1, - - - , N, j=0,1, - - - , m*N-1) arranged in a matrix of N rows.times.(m gradations*N) columns;
- transposition mode calculating means for calculating a maximum value M of a transposition mode L according to a first equation M=[log.sub.2 N] by utilizing the number N of rows or columns of the multivalued source picture image stored in the picture image storing means, the symbol [x] denoting a ceiling function of a constant x in which a value of [x] agrees with a value of the constant x when the constant x equals a positive integer or a value of [x] agrees with an integer determined by raising a decimal fraction of the constant x to a unit when the constant x has the decimal fraction;
- row selecting means for numbering a series of rows of the multivalued source picture image stored in the picture image storing means from a 0-th row to an (N-1)-th row, numbering a series of columns of the multivalued source picture image from a 0-th column to an (m*N-1)-th column, repeatedly selecting an A-th row having a row number A while increasing the row number A in increments of 1 in the range from a minimum value k*2.sup.L of the row number A to a maximum value k*2.sup.L +2.sup.L-1 -1 of the row number A and increasing the loop counting value k in increments of 1 in the range from 0 to N/2.sup.L -1 each time the transposition mode L is increased in increments of 1 in the range from L=1 to the maximum value M of the transposition mode L calculated in the transposition mode calculating means, and repeatedly selecting a B-th row having a row number B according to a second equation B=A+2.sup.L-l each time the A-th row is selected;
- picture image transforming means for representing the picture data placed in the A-th row of the multivalued source picture image by A(j) each time the A-th row is selected in the row selecting means, representing the picture data placed in the B-th row of the multivalued source picture image by B(j) each time the B-th row is selected in the row selecting means, and transforming the multivalued source picture image to a quasi-transposed picture image by transposing one or more pieces of picture data placed in the A-th row according to a third equation B'(j)=A(j+m*2.sup.L-1) in a range of the columns p*m*2.sup.L .ltoreq.j.ltoreq.p*m*2.sup.L +m*2.sup.L-1 -1 while increasing a variable p from 0 to N/2.sup.L -1 in increments of 1, transposing one or more pieces of picture data placed in the B-th row according to a fourth equation A'(j)=B(j-m*2.sup.L-1) in a range of the columns p*m*2.sup.L +m*2.sup.L-1 .ltoreq.j.ltoreq.p*m*2.sup.L +m*2.sup.L -1 while increasing a variable p from 0 to N/2.sup.L -1 in increments of 1, holding each of remaining pieces of picture data placed in the A-th row at the same row and column according to a fifth equation A'(j)=A(j) in a range of the columns p*m*2.sup.L .ltoreq.j.ltoreq.p*m*2.sup.L +m*2.sup.L-1 -1 while increasing a variable p from 0 to N/2.sup.L -1 in increments of 1, holding each of remaining pieces of picture data placed in the B-th row at the same row and column according to a sixth equation B'(j)=B(j) in a range of the columns p*m*2.sup.L +m*2.sup.L-1 .ltoreq.j.ltoreq.p*m*2.sup.L +m*2.sup.L -1 while increasing a variable p from 0 to N/2.sup.L -1 in increments of 1, and regarding the picture data A'(j), B'(j) as pieces of picture data A(j), B(j) renewed each time the A-th row and the B-th row are selected in the row selecting means;
- column order changing means for representing the picture data of the quasi-transposed picture image formed in the picture image transforming means by E(i,j), and transposing the picture data E(i,j) of the quasi-transposed picture image according to a seventh equation F(i, m*j+q)=E(i, m*(N-j-1)+q) in a column range of 0.ltoreq.j.ltoreq.N-1, a row range of 0.ltoreq.i.ltoreq.N-1 and a variable range of 0.ltoreq.q.ltoreq.m-1 to change the order of the picture data E(i,j) arranged in the same row for each of the rows, a destination picture image which is defined as a picture image obtained by rotating the multivalued source picture image 90 degrees in a clockwise direction being formed of the picture data F(i,j);
- displaying means for displaying the destination picture image consisting of the picture data F(i,j) which are produced in the column order changing means;
- and
- central processing means for controlling operations in the picture image storing means, the transposition mode calculating means, the row selecting means, the picture image transforming means, the column orders changing means and the displaying means.