Computer screen image magnification system and method

Claim 3

The method of claim 1 , wherein the first and second magnified image data are each generated using a magnification filter that includes a lowpass filter, a highpass filter, and an adder that generates a weighted sum of image data generated by the lowpass and highpass filters.

Claim 4

The method of claim 2 , wherein the first and second image data generated by the highpass filter are each weighted by a sharpness parameter S prior to summing by the adder with the image data generated by the lowpass filter, where S is a value between 0 and 1.

Claim 5

The method of claim 2 , wherein the lowpass and highpass filters are both wavelet like convolution filters, wherein the lowpass filter has coefficients whose sum is equal to 1, and the highpass filter has coefficients whose sum is equal to zero.

Claim 8

The method of claim 5 , wherein the set of interpolated f k,l values in conjunction with the d i,j values represent a smooth surface that is continuous, and that has a two-dimensional spatial first derivative that is continuous.

Claim 9

The method of claim 6 , wherein the smooth surface represented by the set of interpolated f k,l values in conjunction with the d i,j values has at each of a plurality of locations (k,l) for which an interpolated value is generated a tangent plane that is substantially parallel to a plane formed by adjacent ones of the data points (k,l) corresponding to data values d i,j .

Claim 10

The method of claim 6 , wherein whenever a local contiguous set of the initial data values d i,j all fall on a polynomial surface, the interpolated f k,l values that are located between the initial data points also fall on that same polynomial surface.

Claim 11

The method of claim 6 , wherein the non-zero P k,l coefficients, when summed, have an associated sum equal to 1.

Claim 14

A computer program product for use in conjunction with a computer system having a screen buffer for storing image data and a display device for displaying an image corresponding to the image data stored in the screen buffer, the computer program product comprising a computer readable storage medium and a computer program mechanism embedded therein, the computer program mechanism comprising: a screen image magnification module that has instructions for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region.

Claim 15

A computer program product for use in conjunction with a computer system having a screen buffer for storing image data and a display device for displaying an image corresponding to the image data stored in the screen buffer, the computer program product comprising a computer readable storage medium and a computer program mechanism embedded therein, the computer program mechanism comprising: a screen image magnification module that has instructions for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region.

Claim 16

The computer program product of claim 11 , wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data.

Claim 17

The computer program product of claim 12 , wherein the highpass filtered image data generated by the highpass filter instructions is weighted by a sharpness parameter S prior to summing by the summing instructions with the lowpass filtered image data generated by the lowpass filter instructions, where S is a value between 0 and 1.

Claim 18

The computer program product of claim 12 , wherein the lowpass filter instructions and highpass filter instructions implement lowpass and highpass wavelet like convolution filters, respectively, wherein the lowpass wavelet like convolution filter has coefficients whose sum is equal to 1, and the highpass wavelet like convolution filter has coefficients whose sum is equal to zero.

Claim 19

A computer program product for use in conjunction with a computer system having a screen buffer for storing image data and a display device for displaying an image corresponding to the image data stored in the screen buffer, the computer program product comprising a computer readable storage medium and a computer program mechanism embedded therein, the computer program mechanism comprising: a screen image magnification module that has instructions for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data; and the lowpass filter instructions include instructions for generating an interpolated value for each of a plurality of initially undefined f k,l values in accordance with the filter equation: f k , l = ∑ i , j  P k - 2  ni , l - 2  nj  d i , j wherein n is a positive integer; d i,j are the subset of f k,l values which have defined values prior to the generation of the interpolated f k,l values, such that f 2ni,2nj =d i,j for integer values of i and j that fall within the initial set of image data; P k,l are coefficients, no more than eighteen of which have non-zero values; and each non-zero P k,l coefficient is an integer divided by an integer power of two.

Claim 20

A computer program product for use in conjunction with a computer system having a screen buffer for storing image data and a display device for displaying an image corresponding to the image data stored in the screen buffer, the computer program product comprising a computer readable storage medium and a computer program mechanism embedded therein, the computer program mechanism comprising: a screen image magnification module that has instructions for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data; and the lowpass filter instructions include instructions for generating an interpolated value for each of a plurality of initially undefined f k,l values in accordance with the filter equation: f k , l = ∑ i , j  P k - 2  ni , l - 2  nj  d i , j wherein n is a positive integer; d i,j are the subset of f k,l values which have defined values prior to the generation of the interpolated f k,l values, such that f 2ni,2nj =d i,j for integer values of i and j that fall within the initial set of image data; P k,l are coefficients, no more than eighteen of which have non-zero values; and each non-zero P k,l coefficient is an integer divided by an integer power of two.

Claim 21

The computer program product of claim 15 , wherein the set of interpolated f k,l values in conjunction with the d i,j values represent a smooth surface that is continuous, and that has a two-dimensional spatial first derivative that is continuous.

Claim 22

The computer program product of claim 16 , wherein the smooth surface represented by the set of interpolated f k,l values in conjunction with the d i,j values has at each of a plurality of locations (k,l) for which an interpolated value is generated a tangent plane that is substantially parallel to a plane formed by adjacent ones of the data points (k,l) corresponding to data values d i,j .

Claim 23

The computer program product of claim 16 , wherein whenever a local contiguous set of the initial data values d i,j all fall on a polynomial surface, the interpolated f k,l values that are located between the initial data points also fall on that same polynomial surface.

Claim 24

The computer program product of claim 16 , wherein the non-zero P k,l coefficients, when summed, have an associated sum equal to 1.

Claim 25

The computer program product of claim 19 , wherein the P k,l coefficients used by the lowpass filter instructions have coefficient values corresponding to the filter coefficients shown in FIG. 10 A.

Claim 26

The computer program product of claim 20 , wherein the highpass filter instructions utilize highpass filter coefficients corresponding to the filter coefficients in FIG. 10 B.

Claim 27

The computer program product of claim 15 , wherein the highpass filter instructions include instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and the summing instructions including instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 28

The computer program product of claim 11 , wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 29

The method of claim 1 , wherein the first and second magnified image data are each generated using a lowpass filter, a first highpass filter having filter coefficients weighted by a first sharpness parameter S, a second highpass filter having filter coefficients weighted by a second sharpness parameter T, and an adder that generates a weighted sum of filtered image data generated by the lowpass, first highpass and second highpass filters.

Claim 30

The method of claim 5 , wherein the first and second magnified image data are each generated using a lowpass filter, a first highpass filter having filter coefficients weighted by a first sharpness parameter S, a second highpass filter having filter coefficients weighted by a second sharpness parameter T, and an adder that generates a weighted sum of filtered image data generated by the lowpass, first highpass and second highpass filters.

Claim 31

The method of claim 9 , wherein the P k,l coefficients used by the lowpass filter have coefficient values corresponding to the filter coefficients shown in FIG. 10 A.

Claim 32

The method of claim 26 , wherein the highpass filter utilizes highpass filter coefficients corresponding to the filter coefficients in FIG. 10 B.

Claim 33

The method of claim 10 , wherein the first and second magnified image data are each generated using a lowpass filter, a first highpass filter having filter coefficients weighted by a first sharpness parameter S, a second highpass filter having filter coefficients weighted by a second sharpness parameter T, and an adder that generates a weighted sum of filtered image data generated by the lowpass, first highpass and second highpass filters.

Claim 34

A computer system, comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region.

Claim 35

A computer system, comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region.

Claim 36

The computer system of claim 29 , wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data.

Claim 37

The computer system of claim 30 , wherein the highpass filtered image data generated by the highpass filter instructions is weighted by a sharpness parameter S prior to summing by the summing instructions with the lowpass filtered image data generated by the lowpass filter instructions, where S is a value between 0 and 1.

Claim 38

The computer system of claim 30 , wherein the lowpass filter instructions and highpass filter instructions implement lowpass and highpass wavelet like convolution filters, respectively, wherein the lowpass wavelet like convolution filter has coefficients whose sum is equal to 1, and the highpass wavelet like convolution filter has coefficients whose sum is equal to zero.

Claim 39

The computer program product of claim 30 , wherein the lowpass filter instructions utilize lowpass filter coefficients corresponding to the filter coefficients in FIG. 10A, and the highpass filter instructions utilize highpass filter coefficients corresponding to the filter coefficients in FIG. 10 B.

Claim 40

The computer system of claim 30 , wherein the highpass filter instructions include instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and the summing instructions including instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 41

A computer system comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data; and the lowpass filter instructions include instructions for generating an interpolated value for each of a plurality of initially undefined f k,l values in accordance with the filter equation: f k , l = ∑ i , j  P k - 2  ni , l - 2  nj  d i , j wherein n is a positive integer; d i,j are the subset of f k,l values which have defined values prior to the generation of the interpolated f k,l values, such that f 2ni,2nj =d i,j for integer values of i and j that fall within the initial set of image data; P k,l are coefficients, no more than eighteen of which have non-zero values; and each non-zero P k,l coefficient is an integer divided by an integer power of two.

Claim 42

A computer system comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating highpass filtered image data, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data and the highpass filtered image data; and the lowpass filter instructions include instructions for generating an interpolated value for each of a plurality of initially undefined f k,l values in accordance with the filter equation: f k , l = ∑ i , j  P k - 2  ni , l - 2  nj  d i , j wherein n is a positive integer; d i,j are the subset of f k,l values which have defined values prior to the generation of the interpolated f k,l values, such that f 2ni,2nj =d i,j for integer values of i and j that fall within the initial set of image data; P k,l are coefficients, no more than eighteen of which have non-zero values; and each non-zero P k,l coefficient is an integer divided by an integer power of two.

Claim 43

The computer system of claim 35 , wherein the set of interpolated f k,l values in conjunction with the d i,j values represent a smooth surface that is continuous, and that has a two-dimensional spatial first derivative that is continuous.

Claim 44

The computer system of claim 36 , wherein the smooth surface represented by the set of interpolated f k,1 values in conjunction with the d i,j values has at each of a plurality of locations (k,l) for which an interpolated value is generated a tangent plane that is substantially parallel to a plane formed by adjacent ones of the data points (k,l) corresponding to data values d i,j .

Claim 45

The computer system of claim 36 , wherein whenever a local contiguous set of the initial data values d i,j all fall on a polynomial surface, the interpolated f k,l values that are located between the initial data points also fall on that same polynomial surface.

Claim 46

The computer system of claim 36 , wherein the non-zero P k,l coefficients, when summed, have an associated sum equal to 1.

Claim 47

The computer system of claim 39 , wherein the P k,l coefficients used by the lowpass filter instructions have coefficient values corresponding to the filter coefficients shown in FIG. 10 A.

Claim 48

The computer program product of claim 40 , wherein the highpass filter instructions utilize highpass filter coefficients corresponding to the filter coefficients in FIG. 10 B.

Claim 49

The computer system of claim 35 , wherein the highpass filter instructions including instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and the summing instructions including instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 50

A computer system comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 51

A computer system comprising: a screen buffer for storing image data; a display device for displaying an image corresponding to the image data stored in the screen buffer; a processing unit for executing instructions; and a screen image magnification module that has instructions, executable by the processing unit, for: selecting a first region of the displayed image in accordance with user input; copying image data from the screen buffer to a first buffer, the copied image data corresponding to the first selected region; generating first magnified image data corresponding to a portion of the first selected region and storing the first magnified image data in the screen buffer so as to replace the copied image data; receiving user input that selects a second region of the displayed image, the second selected region overlapping the first selected region; copying image data from the screen buffer to a second buffer, the copied image data corresponding to a combined region that includes both the first and second selected regions; copying the image data stored in the first buffer into a portion of the second buffer corresponding to the first selected region; generating second magnified image data corresponding to a portion of the second selected region and storing the second magnified image data in a portion of the second buffer corresponding to the second selected region; and copying into the screen buffer the image data and second magnified image data in the second buffer corresponding to the combined region; wherein wherein the instructions in the screen image magnification module for generating the first and second magnified image data include lowpass filter instructions for generating lowpass filtered image data, highpass filter instructions for generating first highpass image data using first highpass filter coefficients weighted by a first sharpness parameter S and for generating second highpass image data using second highpass filter coefficients weighted by a second sharpness parameter T, and summing instructions for generating the first magnified image data and the second magnified image data by summing the lowpass filtered image data, first highpass image data and second highpass image data.

Claim 52

The computer system of claim 43 , wherein the lowpass filter instructions include instructions for generating an interpolated value for each of a plurality of initially undefined f k,l values in accordance with the filter equation: f k , l = ∑ i , j  P k - 2  ni , l - 2  nj  d i , j wherein n is a positive integer; d i,j are the subset of f k,i values which have defined values prior to the generation of the interpolated f k,l values, such that f 2ni,2nj =d i,j for integer values of i and j that fall within the initial set of image data; P k,l are coefficients, no more than eighteen of which have non-zero values; and each non-zero P k,l coefficient is an integer divided by an integer power of two.

Claim 53

The computer system of claim 44 , wherein the set of interpolated f k,l values in conjunction with the d i,j values represent a smooth surface that is continuous, and that has a two-dimensional spatial first derivative that is continuous.

Claim 54

The computer system of claim 45 , wherein the smooth surface represented by the set of interpolated f k,l values in conjunction with the d i,j values has at each of a plurality of locations (k,l) for which an interpolated value is generated a tangent plane that is substantially parallel to a plane formed by adjacent ones of the data points (k,l) corresponding to data values d i,j .

Claim 55

The computer system of claim 45 , wherein whenever a local contiguous set of the initial data values d i,j all fall on a polynomial surface, the interpolated f k,l values that are located between the initial data points also fall on that same polynomial surface.

Claim 56

The computer system of claim 45 , wherein the non-zero P k,l coefficients, when summed, have an associated sum equal to 1.

Claim 57

The computer system of claim 48 , wherein the P k,l coefficients used by the lowpass filter instructions have coefficient values corresponding to the filter coefficients shown in FIG. 10 A.

Claim 58

The computer program product of claim 49 , wherein the first highpass filter coefficients utilized by the highpass filter instructions corresponding to the filter coefficients in FIG. 10 B.