Claims Analysis
Total Claims: 65
Claim 1
Independent Claim
62 words
A processing apparatus comprising: a memory having first data stored in accordance with a tile-type address and second data stored in accordance with an array-type address; and means for accessing said memory using one of said tile-type address and said array-type address in response to a first process for processing said first data or a second process for processing said second data.
Claim 2
Dependent Claim
62 words
A processing apparatus comprising: a memory having first data stored in accordance with a tile-type address and second data stored in accordance with an array-type address; and means for accessing said memory using one of said tile-type address and said array-type address in response to a first process for processing said first data or a second process for processing said second data.
Claim 3
Dependent Claim
61 words
A processing apparatus of claim 1 , wherein said means for accessing said memory comprises: a data processor which processes general data; a graphic processor which processes said first and second data according to instructions from said data processor; and an input/output controller which control access to said memory in accordance with one of said tile-type address and said array-type address.
Claim 4
Dependent Claim
39 words
A processing apparatus of claim 2 , wherein in case of said first process, said memory is accessed by converting an array-type address to a tile-type address in order to access data stored in accordance with said array-type address.
Claim 5
Dependent Claim
39 words
A processing apparatus of claim 2 , wherein in case of said second process, said memory is accessed by converting a tile-type address to an array-type address in order to access data stored in accordance with said tile-type address.
Claim 6
Dependent Claim
46 words
A processing apparatus of claim 3 , wherein in case of said first process, whether data are accessed in accordance with said tile-type address or by converting an array-type address to a tile-type address is selected in response to an address of data to be accessed.
Claim 7
Dependent Claim
46 words
A processing apparatus of claim 4 , wherein in case of said second process, whether data are accessed in accordance with said array-type address or by converting a tile-type address to an array-type address is selected in response to an address of data to be accessed.
Claim 8
Dependent Claim
31 words
A processing apparatus of claim 5 , wherein said data access is selected by detecting an address of data to be accessed or a memory region storing data to be accessed.
Claim 9
Dependent Claim
30 words
A processing apparatus of claim 1 , wherein said first process is used for processing image data; and said second process is used for processing data other than image data.
Claim 10
Dependent Claim
30 words
A processing apparatus of claim 1 , wherein said first process is used for processing matrix data; and said second process is used for processing data other than matrix data.
Claim 11
Dependent Claim
31 words
A processing apparatus of claim 1 , wherein the size of a region for first data stored in accordance with said tile-type address is first determined before data access is selected.
Claim 12
Dependent Claim
63 words
A processing apparatus comprising: a memory having first data stored in accordance with a tile-type address and second data stored in accordance with an array-type address; and a processing unit configured to access said memory using a tile-type address or an array-type address in response to a first process for processing said first data or a second process for processing said second data.
Claim 13
Dependent Claim
63 words
A processing apparatus comprising: a memory having first data stored in accordance with a tile-type address and second data stored in accordance with an array-type address; and a processing unit configured to access said memory using a tile-type address or an array-type address in response to a first process for processing said first data or a second process for processing said second data.
Claim 14
Dependent Claim
58 words
A processing apparatus of claim 11 , wherein said processing unit comprises: a data processor which processes general data; a graphic processor which processes said first and second data according to instructions from said data processor; and an input/output controller which control access to said memory in accordance with one of said tile-type address and said array-type address.
Claim 15
Dependent Claim
39 words
A processing apparatus of claim 12 , wherein in case of said first process, said memory is accessed by converting an array-type address to a tile-type address in order to access data stored in accordance with said array-type address.
Claim 16
Dependent Claim
39 words
A processing apparatus of claim 12 , wherein in case of said second process, said memory is accessed by converting a tile-type address to an array-type address in order to access data stored in accordance with said tile-type address.
Claim 17
Dependent Claim
46 words
A processing apparatus of claim 13 , wherein in case of said first process, whether data are accessed in accordance with said tile-type address or by converting an array-type address to a tile-type address is selected in response to an address of data to be accessed.
Claim 18
Dependent Claim
46 words
A processing apparatus of claim 14 , wherein in case of said second process, whether data are accessed in accordance with said array-type address or by converting a tile-type address to an array-type address is selected in response to an address of data to be accessed.
Claim 19
Dependent Claim
30 words
A processing apparatus of claim 15 , wherein data access is selected by detecting an address of data to be accessed or a memory region storing data to be accessed.
Claim 20
Dependent Claim
30 words
A processing apparatus of claim 11 , wherein said first process is used for processing image data; and said second process is used for processing data other than image data.
Claim 21
Dependent Claim
30 words
A processing apparatus of claim 11 , wherein said first process is used for processing matrix data; and said second process is used for processing data other than matrix data.
Claim 22
Dependent Claim
31 words
A processing apparatus of claim 11 , wherein the size of a region for first data stored in accordance with said tile-type address is first determined before data access is selected.
Claim 23
Dependent Claim
45 words
A processing apparatus of claim 11 , wherein said processing unit has a cache memory; data access between said processing unit and said memory is effected via said cache memory; and an addressing mode is charged in response to date stored in said cache memory.
Claim 24
Dependent Claim
167 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein information is recorded in a memory region storing depth information with such a data format that an image located in a deeper position is displayed with a lower resolution; and a luminance calculation is performed for said small region.
Claim 25
Dependent Claim
167 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein information is recorded in a memory region storing depth information with such a data format that an image located in a deeper position is displayed with a lower resolution; and a luminance calculation is performed for said small region.
Claim 26
Dependent Claim
102 words
A shading method of claim 22 , wherein in case plural light sources contributing to luminance calculation for an individual small region in a graphic pattern exist, said small region is composed of plural pixels with its number more than the number of light sources; luminance calculation for an individual light source is performed once in said small region; the number of luminance calculation for an individual pixel is taken to be one or less, and luminance calculation is performed for an individual small region in a single luminance calculation means and in a luminance calculation corresponding to a single light source.
Claim 27
Dependent Claim
93 words
A shading method of claim 23 , wherein a small region partition is defined so as to be shifted pixel by pixel for an individual light source; luminance corresponding to said light source for a top pixel is generated in a said small region; said calculated luminance is defined to be luminance of said pixel in said small region corresponding to said light source, and luminance calculation for plural light sources and pixel generation are performed in a pipe-line mode with said calculated luminance; and luminance calculation is performed for said small region.
Claim 28
Dependent Claim
51 words
A shading method of claim 23 , wherein a one dimensional array defined in a raster direction is defined as a small region; a memory access control is simplified by defining a pixel generation order to be formed in a raster direction; and luminance calculation is performed for said small region.
Claim 29
Dependent Claim
49 words
A shading method of claim 23 , wherein a two dimensional array defined in a tile form is defined as a small region; said small region is resized compactly by defining a pixel generation order to be in zig-zag manner; and luminance calculation is performed for said small region.
Claim 30
Dependent Claim
178 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein said plural geometrical vectors representing said vertex parameters are defined in a polar coordinate system; a normalization process of vectors after an interpolation process is eliminated by means in which three parameters of three-dimensional vector are expressed by two terms; and a luminance calculation is performed for said small region.
Claim 31
Dependent Claim
178 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein said plural geometrical vectors representing said vertex parameters are defined in a polar coordinate system; a normalization process of vectors after an interpolation process is eliminated by means in which three parameters of three-dimensional vector are expressed by two terms; and a luminance calculation is performed for said small region.
Claim 32
Dependent Claim
77 words
A shading method of claim 27 , wherein a polar coordinate value obtained by interpolation of plural geometrical vectors is revised by a single component per a single small region; a component to be revised is altered for a single small region; cosine calculation required for an individual component to calculate a cosine value between a couple of vectors in a polar coordinate system is made effected once; and luminance calculation is performed for said small region.
Claim 33
Dependent Claim
43 words
A shading method of claim 28 , wherein plural geometrical vectors are mapped in another coordinate system while keeping a characteristic property of said geometrical vectors; the amount of luminance calculations is reduced; and a luminance calculation is performed for said small region.
Claim 34
Dependent Claim
96 words
A shading method of claim 28 , wherein in a case where plural light sources contributing to luminance calculation for an individual small region in a graphic pattern exist, said small region is composed of plural pixels with its number more than the number of light sources; a luminance calculation for an individual light source is performed once in said small region; and the number of luminance calculations for an individual pixel is taken to be one or less, and said luminance calculation is performed for an individual small region corresponding to a single light source.
Claim 35
Dependent Claim
92 words
A shading method of claim 30 , wherein a small region partition is defined so as to be shifted pixel by pixel for an individual light source; luminance corresponding to said light source for a top pixel is generated in said small region; said calculated luminance is defined to be luminance of said pixel in said small region corresponding to said light source, and luminance calculation for plural light sources and pixel generation are performed in a pipe-line mode with said calculated luminance; and luminance calculation is performed for said small region.
Claim 36
Dependent Claim
50 words
A shading method of claim 30 , wherein a one-dimensional array defined in a raster direction is defined as a small region; a memory access control is simplified by defining a pixel generation order to be formed in a raster direction; and luminance calculation is performed for said small region.
Claim 37
Dependent Claim
50 words
A shading method of claim 30 , wherein a two dimensional array defined in a tile form is defined as a small region; said small region is resized compactly by defining a pixel generation order to be in a zig-zag manner; and luminance calculation is performed for said small region.
Claim 38
Dependent Claim
81 words
A shading method of claim 33 , wherein by means that a polar coordinate value obtained by interpolation of plural geometrical vectors is revised by a single component per a single small region, and a component to be revised is altered for a single small region, a cosine calculation required for an individual component to calculate a cosine value between a couple of vectors in a polar coordinate system is effected once; and luminance calculation is performed for said small region.
Claim 39
Dependent Claim
209 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein a memory region storing a luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are defined for an individual light source independently of a display region; said mask information is referred to; in case of detecting a shadow region while display a display region, a display image is developed as to reduce a designated luminance component value in said display region; and a luminance calculation is performed for said small region.
Claim 40
Dependent Claim
209 words
A shading method performed in an image display apparatus having at least one image display unit, at least one image data storage unit for storing an image displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defining said image data, said shading method comprising the steps of: calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, wherein a memory region storing a luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are defined for an individual light source independently of a display region; said mask information is referred to; in case of detecting a shadow region while display a display region, a display image is developed as to reduce a designated luminance component value in said display region; and a luminance calculation is performed for said small region.
Claim 41
Dependent Claim
72 words
A shading method of claim 35 , wherein not only a memory region storing a luminance component value is formed, but also a memory region storing an over flow value obtained when calculating a luminance value of a display region is formed by adding a luminance component value; a luminance value of a shadow region is precisely reproduced when an over flow occurs; and luminance calculation is performed for said small region.
Claim 42
Dependent Claim
63 words
A shading method of claim 36 , wherein a memory region storing luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are assigned individually to plural pixels of a display region; the amount of required memory storage due to additive information is reduced; and a luminance calculation is performed for said small region.
Claim 43
Dependent Claim
51 words
A shading method of claim 37 , wherein in case the width of a display region is less than an exponentiation of 2, said additive information is stored in a region having a range equal to an exponentiation of 2 minus 1; and luminance calculation is performed for said small region.
Claim 44
Dependent Claim
194 words
A shading apparatus included in an image display apparatus having at least one image display unit, at least one image data storage unit for storing data for an image to be displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defined by said image data, said shading apparatus calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters defined for an individual graphic pattern and at an individual vertex at said graphic pattern, comprising: defining means for defining plural geometrical vectors as said parameters at said individual vertex; interpolation means for interpolating said plural geometrical vectors in a graphic pattern; and calculation means for calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, said shading apparatus calculating luminance for a small region, wherein said geometrical vectors representing said vertex parameters are defined in a polar coordinate system; a normalization process of vectors after an interpolation process is eliminated by means in which three parameters of three-dimensional vector are expressed by two terms; and a luminance calculation is performed for said small region.
Claim 45
Dependent Claim
194 words
A shading apparatus included in an image display apparatus having at least one image display unit, at least one image data storage unit for storing data for an image to be displayed on said image display unit, and at least one graphic generator for generating a graphic pattern defined by said image data, said shading apparatus calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters defined for an individual graphic pattern and at an individual vertex at said graphic pattern, comprising: defining means for defining plural geometrical vectors as said parameters at said individual vertex; interpolation means for interpolating said plural geometrical vectors in a graphic pattern; and calculation means for calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, said shading apparatus calculating luminance for a small region, wherein said geometrical vectors representing said vertex parameters are defined in a polar coordinate system; a normalization process of vectors after an interpolation process is eliminated by means in which three parameters of three-dimensional vector are expressed by two terms; and a luminance calculation is performed for said small region.
Claim 46
Dependent Claim
92 words
The shading apparatus of claim 39 , wherein plural light sources are provided contributing to luminance calculation for an individual small region in a graphic pattern, said small region is composed of plural pixels in a number more than the number of light sources; luminance calculation for an individual light source is performed once in said small region; and the number of luminance calculations for an individual pixel is taken to be one or less, and a luminance calculation is performed for an individual small region corresponding to a single light source.
Claim 47
Dependent Claim
92 words
The shading apparatus of claim 40 , wherein a small region partition is defined so as to be shifted pixel by pixel for an individual light source; luminance corresponding to said light source for a top pixel is generated in said small region; said calculated luminance is defined to be luminance of said pixel in said small region corresponding to said light source, and luminance calculation for plural light sources and pixel generation are performed in a pipe-line mode with said calculated luminance; and luminance calculation is performed for said small region.
Claim 48
Dependent Claim
51 words
The shading apparatus of claim 40 , wherein a one dimensional array defined in a raster direction is defined as a small region; a memory access control is simplified by defining a pixel generation order to be formed in a raster direction; and luminance calculation is performed for said small region.
Claim 49
Dependent Claim
50 words
The shading apparatus of claim 40 , wherein a two dimensional array defined in a tile form is defined as a small region; said small region is resized compactly by defining a pixel generation order to be in a zig-zag manner; and luminance calculation is performed for said small region.
Claim 50
Dependent Claim
77 words
The shading apparatus of claim 39 , wherein a polar coordinate value obtained by interpolation of plural geometrical vectors is revised by a single component per a single small region; a component to be revised is altered for a single small region; cosine calculation required for an individual component to calculate a cosine value between a couple of vectors in a polar coordinate system is effected once; and a luminance calculation is performed for said small region.
Claim 51
Dependent Claim
47 words
The shading apparatus of claim 44 , wherein plural geometrical vectors are mapped in another coordinate system while keeping a characteristic property of said geometrical vectors; the amount of calculations in a pixel calculation part is reduced; and a luminance calculation is performed for said small region.
Claim 52
Dependent Claim
104 words
The shading apparatus of claim 44 , wherein in a case where plural light sources contributing to luminance calculation for an individual small region in a graphic pattern exist, said small region is composed of plural pixels in a number more than the number of light sources; luminance calculation for an individual light source is performed once in said small region; and the number of luminance calculation for an individual pixel is taken to be one or less, and luminance calculation is performed for an individual small region in a single luminance calculation means and in luminance calculation corresponding to a single light source.
Claim 53
Dependent Claim
92 words
The shading apparatus of claim 46 , wherein a small region partition is defined so as to be shifted pixel by pixel for an individual light source; luminance corresponding to said light source for a top pixel is generated in said small region; said calculated luminance is defined to be luminance of said pixel in said small region corresponding to said light source, and luminance calculation for plural light sources and pixel generation are performed in a pipe-line mode with said calculated luminance; and luminance calculation is performed or said small region.
Claim 54
Dependent Claim
51 words
The shading apparatus of claim 46 , wherein a one dimensional array defined in a raster direction is defined as a small region; a memory access control is simplified by defining a pixel generation order to be formed in a raster direction; and luminance calculation is performed for said small region.
Claim 55
Dependent Claim
49 words
The shading apparatus of claim 46 , wherein a two dimensional array defined in a tile form is defined as a small region; said small region is resized compactly by defining a pixel generation order to be in zig-zag manner; and luminance calculation is performed for said small region.
Claim 56
Dependent Claim
83 words
The shading apparatus of claim 49 , wherein by means in which a polar coordinate value obtained by interpolation of plural geometrical vectors is revised by a single component per a single small region, and a component to be revised is altered for a single small region, a cosine calculation required for an individual component to calculate a cosine value between a couple of vectors in a polar coordinate system is effected once; and a luminance calculation is performed for said small region.
Claim 57
Dependent Claim
226 words
A shading apparatus included in an image display apparatus having at least one image display unit; at least one image data storage unit for storing data for an image to be displayed on said image display unit; and at least one graphic generator for generating a graphic pattern defined by said image data, said shading apparatus calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters defined for an individual graphic pattern and at an individual vertex at said graphic pattern, comprising: defining means for defining plural geometrical vectors as said parameters at said individual vertex; interpolation means for interpolating said plural geometrical vectors in a graphic pattern; and calculation means for calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, said shading apparatus calculating luminance for a small region, wherein a memory region storing a luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are defined for an individual light source independently of a display region; said mask information is referred to; in case of detecting a shadow region while displaying a display region, a display image is developed as to reduce a designated luminance component value in said display region; and a luminance calculation is performed for said small region.
Claim 58
Dependent Claim
226 words
A shading apparatus included in an image display apparatus having at least one image display unit; at least one image data storage unit for storing data for an image to be displayed on said image display unit; and at least one graphic generator for generating a graphic pattern defined by said image data, said shading apparatus calculating parameters, each defining luminance at an individual pixel forming said graphic pattern, said parameters defined for an individual graphic pattern and at an individual vertex at said graphic pattern, comprising: defining means for defining plural geometrical vectors as said parameters at said individual vertex; interpolation means for interpolating said plural geometrical vectors in a graphic pattern; and calculation means for calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation, said shading apparatus calculating luminance for a small region, wherein a memory region storing a luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are defined for an individual light source independently of a display region; said mask information is referred to; in case of detecting a shadow region while displaying a display region, a display image is developed as to reduce a designated luminance component value in said display region; and a luminance calculation is performed for said small region.
Claim 59
Dependent Claim
72 words
The shading apparatus of claim 51 , wherein not only a memory region storing a luminance component value is formed, but also a memory region storing an over flow value obtained when calculating a luminance value of a display region is formed by adding a luminance component value; a luminance value of a shadow region is precisely reproduced when an over flow occurs; and luminance calculation is performed for said small region.
Claim 60
Dependent Claim
64 words
The shading apparatus of claim 52 , wherein a memory region storing a luminance component value and a memory region storing mask information representing a shadow region against its corresponding light source are assigned individually to plural pixels of a display region; the amount of required memory storage due to additive information is reduced; and a luminance calculation is performed for said small region.
Claim 61
Dependent Claim
53 words
The shading apparatus of claim 53 , wherein in case where the width of a display region is less than an exponentiation of 2, said additive information is stored in a region having a range equal to an exponentiation of 2 minus 1; and a luminance calculation is performed for said small region.
Claim 62
Dependent Claim
48 words
The shading apparatus of claim 54 , wherein said information is recorded in a memory region storing depth information with such a data format that an image located in a deeper position is displayed with a lower resolution; and a luminance calculation is performed for said small region.
Claim 63
Dependent Claim
99 words
A processing apparatus of claim 11 , further comprising a shading unit for adding shading to data processed by said processing unit, said shading being performed by: calculating parameters, each defining luminance at an individual pixel forming a graphic pattern, said parameters being defined for an individual graphic pattern and at an individual vertex at said graphic pattern, wherein plural geometrical vectors are defined as said parameters at said individual vertex; interpolating said plural geometrical vectors in a graphic pattern; and calculating luminance for a small region in a graphic pattern by using plural geometrical vectors generated by interpolation.
Claim 64
Dependent Claim
104 words
A processing apparatus of claim 11 , further comprising a shading unit for adding shading to data processed by said processing unit, by calculating luminance for a small region in a graphic pattern defined by said data parameters, said shading unit comprising: defining means for defining plural geometrical vectors as parameters each defining luminance at an individual pixel forming said graphic pattern at an individual vertex at said graphic pattern; interpolation means for interpolating said plural geometrical vectors in said graphic pattern; and calculation means for calculating luminance for said small region in a graphic pattern by using plural geometrical vectors generated by interpolation.
Claim 65
Dependent Claim
103 words
A processing apparatus of claim 1 , further comprising shading means for adding shading to data processed by said processing unit, by calculating luminance for a small region in a graphic pattern defined by said data parameters, said shading means comprising: defining means for defining plural geometrical vectors as parameters each defining luminance at an individual pixel forming said graphic pattern at an individual vertex at said graphic pattern; interpolation means for interpolating said plural geometrical vectors in said graphic pattern; and calculation means for calculating luminance for said small region in a graphic pattern by using plural geometrical vectors generated by interpolation.