1. A toner for developing electrostatic images comprising toner mother particles, and an external additive, wherein:
the average of shape factors SF1 of the toner mother particles represented by the following Formula (1) is 140 or less;
the external additive contains higher alcohol particles having a volume-average particle diameter of 1 to 12 \u03bcm; and
the content of the higher alcohol particles having a diameter equal to or less than the volume-average particle diameter of the toner mother particles is in a range of 0.15 to 2.5 parts by weight with respect to 100 parts by weight of the toner mother particles:
SF1=(L2A)\xd7(\u03c04)\xd7100\u2003\u2003Formula (1)
wherein L represents the maximum length of each toner mother particle; and A represents the projected area of each toner mother particle.
2. A toner according to claim 1, wherein the average of shape factor SF1 of the higher alcohol particles is equal to or more than 140.
3. A toner according to claim 1, wherein the higher alcohol particles has 16 to 150 carbon atoms.
4. A toner according to claim 1, wherein a preparation of the higher alcohol particles includes pulverization.
5. A toner according to claim 1, wherein a volume-average particle diameter of the toner mother particles is 2 to 12 \u03bcm.
6. A toner according to claim 1, further including inorganic oxide particles having a volume-average particle diameter of 20 to 300 nm.
7. A toner according to claim 1, further including monodisperse spherical silica having a true specific density of 1.3 to 1.9 and a volume-average particle diameter of 80 to 300 nm.
8. A toner according to claim 1, further including monodisperse spherical silica, the standard deviation of which is a value of volume-average particle diameter D50 multiplied by 0.22 or less.
9. A toner according to claim 1, further including monodisperse spherical silica, the Wadell sphericity of which is 0.6 or more.
10. A developer for developing electrostatic charged images comprising a toner for developing electrostatic charged images, wherein:
the toner comprises at least toner mother particles containing a binder resin and a colorant, and an external additive;
the average of the shape factors SF1 of the toner mother particles represented by the following Formula (1) is 140 or less;
the external additive further comprises higher alcohol particles having a volume-average particle diameter 1 to 12 \u03bcm; and
the content of the higher alcohol particles having a diameter equal to or less than the volume-average particle diameter of the toner mother particles is in a range of 0.15 to 2.5 parts by weight with respect to 100 parts by weight of the toner mother particles:
SF=(L2A)\xd7(\u03c04)\xd7100\u2003\u2003Formula (1)
wherein L represents the maximum length of each toner mother particle; and A represents the projected area of each toner mother particle.
11. A developer according to claim 10, further comprising a resin-coated carrier.
12. A developer according to claim 10, further comprising a carrier having the volume-average particle diameter of core materials of 10 to 100 \u03bcm.
13. An image forming method using a toner for developing electrostatic charged images, comprising:
charging a photoreceptor to form a latent image on a latent image bearing body;
developing the latent image on a developer bearing body by using the toner for developing electrostatic charged images and transferring the developed image; and
cleaning comprising removing the remaining toner on the latent image bearing body, wherein
the toner comprises at least toner mother particles containing a binder resin and a colorant, and an external additive;
the average of the shape factors SF1 of the toner mother particles represented by the following Formula (1) is 140 or less;
the external additive further comprises higher alcohol particles having a volume-average particle diameter 1 to 12 \u03bcm; and
the content of the higher alcohol particles having a diameter equal to or less than the volume-average particle diameter of the toner mother particles is in a range of 0.15 to 2.5 parts by weight with respect to 100 parts by weight of the toner mother particles:
SF1=(L2A)\xd7(\u03c04)\xd7100\u2003\u2003Formula (1)
wherein L represents the maximum length of each toner mother particle; and A represents the projected area of each toner mother particle.
14. An image forming method according to claim 13, wherein charging is conducted by contact-type electrostatic charging.
15. An image forming method according to claim 13, wherein cleaning is conducted by blade cleaning.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A computer-implemented method for separating a tooth from adjacent structure, comprising:
identifying a line between the tooth and the adjacent structure;
defining a closed cutting surface that passes through the line between the tooth and the adjacent structure and that creates an approximate shape of a root of the tooth; and
applying the cutting surface between the tooth and the structure to separate the tooth from the structure in a single cut.
2. The method of claim 1, wherein the cutting surface is curved.
3. The method of claim 1, wherein the cutting surface is expressed as a function.
4. The method of claim 1, wherein the cutting surface is expressed as a spline function and a quadratic function.
5. The method of claim 1, wherein the cutting surface is expressed as a spline function and a parabolic function.
6. The method of claim 1, wherein the cutting surface is interactively adjusted.
7. The method of claim 4, wherein the interactive adjustment of the cutting surface modifies a function defining the cutting surface.
8. The method of claim 4, further comprising interactively highlighting the separated portion.
9. The method of claim 8, further comprising interactively highlighting the border of the separated portion.
10. The method of claim 1, wherein the cutting surface is defined by specifying a basis for the tooth.
11. The method of claim 1, wherein the structure is a gingiva, further comprising finding a line between a tooth surface and the gingiva and applying the cutting surface to said line.
12. The method of claim 11, further comprising finding a high curvature location on the tooth surface.
13. The method of claim 11, further comprising fitting a spline to the line.
14. The method of claim 1, wherein the cutting surface further comprises a plurality of surfaces.
15. The method of claim 14, wherein the root of the tooth is modeled as a parabolic surface below a gingival line.
16. The method of claim 14, further comprising defining an enclosing surface to enclose the crown of the tooth.
17. The method of claim 14, further comprising:
displaying the surface specified with a plurality of nodes;
adjusting one or more nodes to modify the surface; and
applying the surface to separate the gingiva from the tooth.
18. The method of claim 17, further comprising providing a handle to adjust each orientation of the cutting shape.
19. The method of claim 17, wherein adjusting one or more nodes further comprises moving one or more nodes.
20. The method of claim 17, wherein the cutting surface is formed using a function in a cylindrical coordinate system.
21. A system for separating a tooth from adjacent structure, comprising:
means for identifying a line between the tooth and the adjacent structure;
means for defining a closed cutting surface that passes through the line between the tooth and the adjacent structure and that creates an approximate shape of a root of the tooth; and
means for applying the cutting surface between the tooth and the structure to separate the tooth from the structure in a single cut.
22. A computer program, residing on a tangible storage medium, for use in separating a computer model of a tooth from a computer model of a dental structure, the program comprising executable instructions operable to cause a computer to:
identify a line between the tooth and the structure;
define a closed cutting surface that passes through the line between the tooth and the structure and that creates an approximate shape of a root of the tooth; and
apply the cutting surface between the tooth and the structure to separate the tooth from the structure in a single cut,
wherein applying the cutting surface includes reconstructing a root of the tooth.
23. A computer program, residing on a tangible storage medium, for use in separating a computer model of a tooth from a computer model of a dental structure, the program comprising executable instructions operable to cause a computer to:
identify a line between the tooth and the structure;
define a closed cutting surface that passes through the line between the tooth and the structure and that creates an approximate shape of a root of the tooth; and
apply the cutting surface between the computer model of the tooth and the computer model of the dental structure to separate the computer model in a single cut.
24. A computer, comprising:
a processor;
a data storage device coupled to the processor, the data storage device containing code for use in separating a computer model of a tooth from a computer model of an adjacent dental structure, the program comprising executable instructions operable to cause a computer to:
identify a line between the tooth and the structure;
define a closed cutting surface that passes through the line between the tooth and the structure, wherein the cutting surface is expressed as a spline function and a quadratic function and wherein the cutting surface further comprises a plurality of surfaces and wherein the root of the tooth is modeled as a parabolic surface below a gingival line; and
apply the cutting surface to the tooth to separate the tooth from the dental structure in a single cut.
25. The system of claim 24, further comprising instructions to define an enclosing surface to enclose the crown of the tooth.