Sphere 2
Author: c | 2025-04-25
The 0-sphere is a pair of points on the line, the 1-sphere is a circle in the plane, and the 2-sphere is an ordinary sphere within 3-dimensional space. 2-sphere wireframe as an orthogonal projection, Source Code
Sphere-2/content.html at main coder5676/Sphere-2 - GitHub
Degrees • EX: +2.00+1.00x080 +3.00-1.00x170 The purpose of transposition is to change the same prescription into a different formTransposition 1 Minute Drill • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees • 1. + 1.75 – 0.75 X 030 • 2. – 2.25 + 1.00 X 170 • 3. – 1.75 + 2.00 X 125Transposition 1 Minute Drill • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees • 1. + 1.75 – 0.75 X 030 a. + 1.00 + 0.75 X 120 • 2. – 2.25 + 1.00 X 170 a. – 1.25 – 1.00 X 080 • 3. – 1.75 + 2.00 X 125 a. + 0.25 – 2.00 X 035Spherical Equivalent -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only EX. -2.00 -0.50 X 145 (half the cylinder) -0.25 (add to sphere) 0.25 + 2.00 Answer: -2.25 SphSpherical Equivalent 1 Minute drill -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only 1. – 2.25 – 1.00 X 120 2. + 1.00 – 2.00 X 090 3. + 0.75 – 1.50 X 150 Spherical Equivalent 1 Minute drill -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only 1. – 2.25 – 1.00 X 120 a. – 1.75 Sph 2. + 1.00 – 2.00 X 090 b. – 1.00 Sph 3. + 0.75 – 1.50 X 150 c. Plano (no glasses)Prescriptions: Decentration • Decentration calculations • Eye size plus distance between lenses minus patient’s PD divided by 2. • Example: 52-20-145 pt PD 62 • 52+ 20 – 62 = 10 / 2 = 5 Remember the measurements are in mmDecentration 1 minute Minus cylinder notation: +5.00 -2.00 x 180 + 5.00 Hint: The sphere is “married” to the axis; the cylinder is the distance between the numbers on the crossPrescriptions: Transposition • Transposition • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees Hint: When combining positive and negative numbers, think in terms of money. Example: -2.00 combined with +0.50 If you are $2.00 “in the hole” and you deposit $0.50, what is your balance? Answer: $1.50 “in the hole”, or -1.50.Components of an Optical Prescription • Axis • The number in the axis block indicates where the sphere meridian is located on a 180° circlePrescriptions: Transposition • -1.00 +2.00 X 160 • +1.25 -0.75 x 030 • Plano +1.00 x 090 • +1.00 -2.00 x 070 • +0.50 +0.75 x 120 • +1.00 -1.00 x 180 Transposition ExamplesOptical Cross - 2.50 - 4.50 • To take an RX off the Optical Cross in Minus Cylinder Form: • Step 1 Start with the most plus sphere power (use your number line) • Step 2 Your axis is “married” to your sphere • Step 3 Your cylinder is the distance traveled between the sphere and number 90 degrees away - 1.25 +1.50 121 090 031 180 Find the answers to the above equations, you 1 minute Optical Cross - 2.50 - 4.50 • To take an RX off the Optical Cross in Minus Cylinder Form: • Step 1 Start with the most plus sphere power (use your number line) • Step 2 Your axis is “married” to your sphere • Step 3 Your cylinder is the distance traveled between the sphere and number 90 degrees away - 1.25 +1.50 121 090 031 180 L -1.25 – 3.25 X 090 R +1.50 – 4.00 X 121 Find the answers to the above equationsTransposition • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90Is there an Odin Sphere 2? - Odin Sphere Leifthrasir - GameFAQs
• - 0.75 – 1.00 X 150 • Add 2.00 • New Rx +0.50 -1.50 X 035 • +1.25 – 1.00 X 150 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisConvert to SVN or Near Rx only 1 min drill • + 3.25 – 0.75 X 125 • + 1.75 – 1.00 X 090 • Add 2.50 • - 4.50 – 1.50 X 035 • - 1.75 – 1.00 X 150 • Add 2.00 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisConvert to SVN or Near Rx only • + 3.25 – 0.75 X 125 • + 1.75 – 1.00 X 090 • Add 2.50 • New Rx +5.75 -0.75 X 125 • +4.25 – 1.00 X 090 • - 4.50 – 1.50 X 035 • - 1.75 – 1.00 X 150 • Add 2.00 • New Rx -2.50 -1.50 X 035 • +0.25 – 1.00 X 150 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisMath Formulas Cont… • Prentiss Rule • Convert focal length to Diopters • Convert diopters length to focal • Convert to Near Rx • Transpose plus/minus cylinder • Calculate the optical cross • Calculate decentrationReview Questions 3 minutes • -1.00 -1.00 x 090 transpose Answer______________ • - 0.50 -2.00 x 008 transpose Answer______________ • -1.00 -1.50 x 160 transpose Answer______________ • - 5.00 -3.00 x 088 transpose Answer______________ • -3.00 -1.50 x 095 transpose Answer______________ • - 2.50 + 1.50 x 103 transpose Answer______________ • -1.00 + 0.50 x 162 transpose Answer______________ • + 2.50 + 2.50 x 103 transpose Answer______________ • -2.50 + 1.00 x 029 transpose Answer______________Review Questions • -1.00 -1.00 x 090 transpose Answer -2.00 + 1.00. The 0-sphere is a pair of points on the line, the 1-sphere is a circle in the plane, and the 2-sphere is an ordinary sphere within 3-dimensional space. 2-sphere wireframe as an orthogonal projection, Source CodeTriangulations of the Sphere (Part 2)
Of the body is given by$V = - \dfrac{{GM}}{r}$Gravitational potential is a scalar quantity.The gravitational potential in the SI unit is J kg and in the CGS system is $erg{g^{ - 1}}$.Gravitational potential (V) is related with gravitational field intensity(E) by a relation$E = - \dfrac{{dV}}{{dr}}$Gravitational Field Intensity and Gravitational potential Fue to a Spherical Shell:The gravitational field intensity and gravitational potential due to a spiritual shell of radius R and mass M at a point distant r from the centre of the shell is given as follows: Gravitational Field Intensity and Gravitational Potential Due To A Spherical Shell.At a point outside the shell i.e. r > a${E_{outside}} = - \dfrac{{GM}}{{{r^2}}}$, ${V_{outside}} = - \dfrac{{GM}}{r}$At a point on the surface of the shell i.e. r = a${E_{surface}} = - \dfrac{{GM}}{{{a^2}}}$,${V_{surface}} = - \dfrac{{GM}}{a}$At a point inside the shell i.e. r ${E_{inside}} = 0$, ${V_{inside}} = - \dfrac{{GM}}{a}$Gravitational Field Intensity and Gravitational Potential Due To A Solid Sphere:The gravitational field intensity and gravitational potential duty a solid sphere of radius R and mass M at a distance r from the centre of the sphere is given as follows: Gravitational Field Intensity and Gravitational Potential Due to a Solid SphereAt a point outside the sphere, i.e. r > a${E_{outside}} = - \dfrac{{GM}}{{{r^2}}}$ ${V_{outside}} = - \dfrac{{GM}}{r}$At a point on the surface of the sphere, i e. r = a${E_{surface}} = - \dfrac{{GM}}{{{a^2}}}$ ${V_{surface}} = - \dfrac{{GM}}{a}$At a point inside the sphere, i.e. r ${E_{inside}} = - \dfrac{{GMr}}{{{a^3}}}$, ${V_{inside}} = - \dfrac{{GM\left( {3{a^2} A blurring operation. Theoretically, it is important that the mask does not introduce high-frequency correlations between the two half maps. Only building blurred masks helps reduce the chance of this happening.Open the volume in ChimeraX. This example uses the results of a non-uniform refinement. For all commands in this example, the base volume is volume #1.Blur the volume using a Gaussian filter: volume gaussian #1 sDev 2. Increasing the value for sDev will make the map more blurry. This command creates a new, blurred volume. The blurred base volume is volume #2.Step 2: Create copies of the blurred volumeSince the volume eraser tool directly modifies the volume it operates on, you must create another copy of the blurred volume if you plan on creating a mask for Particle subtraction.Copy the map with volume copy #2Step 3: Erase the region outside the desired maskIn this step, we will erase the regions outside the mask using the Volume Eraser tool. This tool creates a sphere and allows you to erase everything either inside or outside the sphere. There is no undo function for this tool, so be careful when erasing volumes. You can create copies of the volume as you go if the process is long and complicated using volume copy as above.Open the volume eraser tool: Right Mouse ribbon menu > Erase. You should see a sphere appear. Holding down right-click and dragging your mouse moves the sphere. Erasing inside or outside the sphere is accomplished with the buttons in theSphere 2 Announced - MMORPG.com
Punch! CAD » ViaCAD & Shark » Rendering & Display » ViaCAD Pro 7 Rendering problem (#4518) nanoplane #1 Posted : Saturday, September 29, 2012 11:08:16 AM(UTC) Rank: Junior MemberJoined: 7/1/2009(UTC)Posts: 4 I'm on MacOS 10.8.2 and photo rendering just doesn't seem to work. I just get a Black shape on the resulting screen, no detail, no reflections, no color, just black...What Might I be doing wrong?? WWW jol #2 Posted : Saturday, September 29, 2012 2:20:02 PM(UTC) Rank: Senior MemberJoined: 2/26/2007(UTC)Posts: 2,156Was thanked: 1 time(s) in 1 post(s) Check your monitor's on first - sorry !HmmNot sure - can you go back to the simplest scenario - restart the app, draw a sphere and render - will it give you a result then ? nanoplane #3 Posted : Saturday, September 29, 2012 4:21:46 PM(UTC) Rank: Junior MemberJoined: 7/1/2009(UTC)Posts: 4 :-).. monitor is on..Going back to basics.. if all I do is create a sphere, I get somewhat reasonable but unexpected results..."User Specified" render's the sphere in the color I selected and for the most part, some of the attributes make sense.Metal, Plastic, Glass and Mirror give unexpected results.. Metal comes out as a gold color, seems to be reflecting some image that I haven't defined anywhere I can tell. (checked the render settings, foreground and background set as none)Glass renders as a black sphere with no detailPlastic renders as an almost black sphere with some evidence of reflection of that same image as metal.Mirror gives me a render similar to Metal.Sketch is just weird. Sphere is solid color, no highlights .And....If I add another body to the drawing (say a cylindrical pedestal for the Sphere), That second body comes out black in all views except metal and mirror. WWW jol #4 Posted : Saturday, September 29, 2012 5:39:51 PM(UTC) Rank: Senior MemberJoined: 2/26/2007(UTC)Posts: 2,156Was thanked: 1 time(s) in 1 post(s) I suspect things are different in ViaCAD - I'm using Shark and seem to get better results than you.These used to be called 'Rapid-render Presets' - a name that explained well what they didNow they have no name except for "Glass" - it makes it look like this is all you can do with this renderer - which I assure you is not the case.If you want better results, don't use the presets - as they are just quick and dirty and they give you what they give you.The charge of sphere $2$ is twice that of sphere $1$. cen - Quizlet
Backstreet's back and they're headed to the Strip. Well, to be more specific they're headed to The Sphere. Legendary boy band the Backstreet Boys have announced a summer residency at the famous Sphere in Las Vegas, the 18,600 seat venue that first opened in 2023. Previous acts who have had residencies at The Sphere include Dead & Company, U2 and The Eagles, but the Backstreet Boys will be the first pop act to hold court at the state-of-the-art venue. Performances will run between July 11 – Aug. 17, 2025, with the band promising to "do things we could have never have imagined back in ’99." For everything you need to know about the Backstreet Boys residency at The Sphere, including how to get tickets for newly-added concert dates, read on.When will the Backstreet Boys perform at The Sphere?The five original members of the Backstreet Boys — Nick Carter, Howie Dorough, AJ McLean, Brian Littrell and Kevin Richardson — will be performing at The Sphere in Las Vegas. Performance dates are July 11, 12, 13, 18, 19, 20, 25, 26 and 27, and August 1, 2, 3, 8, 9, 10, 15, 16, and 17, 2025..When do tickets for the Backstreet Boys "Into the Millennium" shows at The Sphere go on sale?Tickets, including concert-hotel packages, for the Backstreet Boys Sphere dates between July 11 – Aug. 10 are currently on sale at Ticketmaster. Tickets for three newly-added dates, Aug. 15, 16, and 17, will first be available via the Backstreet Boys Fan Club Presale beginning Tuesday, February 25 at 12 p.m. ET. Fans who previously signed up for the Artist Presale can access it beginning Wednesday, February 26 at 12 p.m. ET. The general on sale will begin Friday, February 28 at 9am PT at backstreetboys.com and Ticketmaster.Sign up on TicketmasterBackstreet Boys Sphere residency ticket cost:Individual ticket prices for the remaining seats at the Backstreet Boys residency at The Sphere start around $320 to $400 depending on show date, and run all the way up to $1,200. There are also tickets starting between $133 and $184 depending on the show on StubHub.. The 0-sphere is a pair of points on the line, the 1-sphere is a circle in the plane, and the 2-sphere is an ordinary sphere within 3-dimensional space. 2-sphere wireframe as an orthogonal projection, Source Code What is a Sphere? 2. Sphere Formulas: 3. Properties of Sphere: 4. Circumference of a Sphere: 5. Difference between Circle and Sphere: 6. FAQs on Sphere: What is a Sphere? In geometrySphere sphere sphere by Best_codes
At the Traveling Firm/Agency.=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=11.0 - SCRIPTS IN JAPANESE AL BHED[NOTE: This is incomplete! It's SO under construction!] The Japanese script in Final Fantasy X. Do note that if the text is blue, it is inAl Bhed. If the text is red, that means that it is translated or it is a keyword. This isso that you can recap on what the Al Bhed's say and you can read it for your enjoyment.The Japanese is translated to the best of my knowledge. [They have a 20% of being wrong!So you can trust my translations!] I'm not fluent, but I taught myself Japanese for fiveyears and damned proud of the translations I do. I also provided the Roumaji. ^^;; :DIALOGUE LEGEND - What each of these means!:"" = Words spoken with brackets in between means they are speaking in Al Bhed. [NOTE: The keywords are taken out of brackets!]"..." = Words spoken with quotations are spoken in Japanese.^-"..." = Words spoken with ^- are translated from Japanese into English.=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=MARINE RUINS / Upper right path, blue sphere on pillar:DIALOGUE:-BLUE SPHERE : " "Makaraanya ""TRANSLATION:-BLUE SPHERE : "Ikazuchi ga taemanaku furisosogi basho ni te "Makaraanya wo seki yottsume no touno "Migigawa wo miyo" ^- "Thunder will continually to fall and downpour on the location ^- "Where Maklarna is the fourth gate ^- "You can see on the right side"=-=-=-=-=-=-=-=-=MARINE RUINS / Upper left path, blue sphere on ground:DIALOGUE:-BLUE SPHERE : " Aru Bedo Go " TRANSLATION:-BLUE SPHERE : "Mezase! Aru Bedo Go Masutaa! Kentou wo inoru!" ^- "Alright! Al Bhed Master! I pray you good luck!"=-=-=-=-=-=-=-=-=AL BHED SYNTHETIC SPHERE / Whenever you are using it:DIALOGUE:-POPUP WINDOW : [ARU BEDO GO ??? GOUSEI SUFIA]-POPUP WINDOW : {Memorii Kaado (PS2) ni Seebu shita [FINAL FANTASY X] no deeta kara Aru Bedo Go ??? no deeta wo go mikon de Aru Bedo Go ??? wo gousei suru koto ga de kimasu!}-POPUP WINDOW : {Surotto wo ??? shiteku da sai.}-OPTIONS : *- [Surotto 1] *- [Surotto 2] *- [Kyanseru]-CHECKING : {Surotto 1 - 2 tomo ni Memorii Kaado (PS2) ya kontoroura no mesa sashita ikuwasu disukutorei wo ake nai de da sai}-FINISHED : {Aru Bedo Go ??? No ?? mikomi ni ??? shimashita!}-POPUP WINDOW : {Aru Bedo Go ??? wo gousei shimasuka?}-OPTIONS : *- [Hai] *- [Iie]TRANSLATION:-[TRANSLATION COMING SOON!]=-=-=-=-=-=-=-=-=MARINE RUINS / After killing the monster, Click:DIALOGUE:-ROPP : ""-IONON : "Mamono "-AL BHED FAMILY : ""-NEDUS : ""-???? : ""-NEDUS : ""-???? : ""-???? : ""TRANSLATION:-ROPP : "Koitsu nani mono da?" ^- "Who is this guy?"-IONON : "Mamono da! Ningen ni baketerun da!" ^- "A monster! Disguised as a human!"-AL BHED FAMILY : "Sou da! Sou ni kimatteru" ^- "I see! Then it's decided!"-NEDUS : "Yacchi mauka!?" ^- "WannaComments
Degrees • EX: +2.00+1.00x080 +3.00-1.00x170 The purpose of transposition is to change the same prescription into a different formTransposition 1 Minute Drill • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees • 1. + 1.75 – 0.75 X 030 • 2. – 2.25 + 1.00 X 170 • 3. – 1.75 + 2.00 X 125Transposition 1 Minute Drill • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees • 1. + 1.75 – 0.75 X 030 a. + 1.00 + 0.75 X 120 • 2. – 2.25 + 1.00 X 170 a. – 1.25 – 1.00 X 080 • 3. – 1.75 + 2.00 X 125 a. + 0.25 – 2.00 X 035Spherical Equivalent -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only EX. -2.00 -0.50 X 145 (half the cylinder) -0.25 (add to sphere) 0.25 + 2.00 Answer: -2.25 SphSpherical Equivalent 1 Minute drill -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only 1. – 2.25 – 1.00 X 120 2. + 1.00 – 2.00 X 090 3. + 0.75 – 1.50 X 150 Spherical Equivalent 1 Minute drill -Step 1 Take half the cylinder and add algebraically to sphere - Step 2 Drop the cylinder and axis and write sphere only 1. – 2.25 – 1.00 X 120 a. – 1.75 Sph 2. + 1.00 – 2.00 X 090 b. – 1.00 Sph 3. + 0.75 – 1.50 X 150 c. Plano (no glasses)Prescriptions: Decentration • Decentration calculations • Eye size plus distance between lenses minus patient’s PD divided by 2. • Example: 52-20-145 pt PD 62 • 52+ 20 – 62 = 10 / 2 = 5 Remember the measurements are in mmDecentration 1 minute
2025-03-27Minus cylinder notation: +5.00 -2.00 x 180 + 5.00 Hint: The sphere is “married” to the axis; the cylinder is the distance between the numbers on the crossPrescriptions: Transposition • Transposition • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90 degrees Hint: When combining positive and negative numbers, think in terms of money. Example: -2.00 combined with +0.50 If you are $2.00 “in the hole” and you deposit $0.50, what is your balance? Answer: $1.50 “in the hole”, or -1.50.Components of an Optical Prescription • Axis • The number in the axis block indicates where the sphere meridian is located on a 180° circlePrescriptions: Transposition • -1.00 +2.00 X 160 • +1.25 -0.75 x 030 • Plano +1.00 x 090 • +1.00 -2.00 x 070 • +0.50 +0.75 x 120 • +1.00 -1.00 x 180 Transposition ExamplesOptical Cross - 2.50 - 4.50 • To take an RX off the Optical Cross in Minus Cylinder Form: • Step 1 Start with the most plus sphere power (use your number line) • Step 2 Your axis is “married” to your sphere • Step 3 Your cylinder is the distance traveled between the sphere and number 90 degrees away - 1.25 +1.50 121 090 031 180 Find the answers to the above equations, you 1 minute Optical Cross - 2.50 - 4.50 • To take an RX off the Optical Cross in Minus Cylinder Form: • Step 1 Start with the most plus sphere power (use your number line) • Step 2 Your axis is “married” to your sphere • Step 3 Your cylinder is the distance traveled between the sphere and number 90 degrees away - 1.25 +1.50 121 090 031 180 L -1.25 – 3.25 X 090 R +1.50 – 4.00 X 121 Find the answers to the above equationsTransposition • Step 1 = Combine the sphere and cylinder power mathematically • Step 2 = Change the sign of the cylinder • Step 3 = Change the axis by 90
2025-04-07• - 0.75 – 1.00 X 150 • Add 2.00 • New Rx +0.50 -1.50 X 035 • +1.25 – 1.00 X 150 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisConvert to SVN or Near Rx only 1 min drill • + 3.25 – 0.75 X 125 • + 1.75 – 1.00 X 090 • Add 2.50 • - 4.50 – 1.50 X 035 • - 1.75 – 1.00 X 150 • Add 2.00 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisConvert to SVN or Near Rx only • + 3.25 – 0.75 X 125 • + 1.75 – 1.00 X 090 • Add 2.50 • New Rx +5.75 -0.75 X 125 • +4.25 – 1.00 X 090 • - 4.50 – 1.50 X 035 • - 1.75 – 1.00 X 150 • Add 2.00 • New Rx -2.50 -1.50 X 035 • +0.25 – 1.00 X 150 • Step 1 • Add the add power to the sphere power and write it as the new sphere power • Step 2 • Write the new complete Rx Sph, Cyl, and AxisMath Formulas Cont… • Prentiss Rule • Convert focal length to Diopters • Convert diopters length to focal • Convert to Near Rx • Transpose plus/minus cylinder • Calculate the optical cross • Calculate decentrationReview Questions 3 minutes • -1.00 -1.00 x 090 transpose Answer______________ • - 0.50 -2.00 x 008 transpose Answer______________ • -1.00 -1.50 x 160 transpose Answer______________ • - 5.00 -3.00 x 088 transpose Answer______________ • -3.00 -1.50 x 095 transpose Answer______________ • - 2.50 + 1.50 x 103 transpose Answer______________ • -1.00 + 0.50 x 162 transpose Answer______________ • + 2.50 + 2.50 x 103 transpose Answer______________ • -2.50 + 1.00 x 029 transpose Answer______________Review Questions • -1.00 -1.00 x 090 transpose Answer -2.00 + 1.00
2025-04-07Of the body is given by$V = - \dfrac{{GM}}{r}$Gravitational potential is a scalar quantity.The gravitational potential in the SI unit is J kg and in the CGS system is $erg{g^{ - 1}}$.Gravitational potential (V) is related with gravitational field intensity(E) by a relation$E = - \dfrac{{dV}}{{dr}}$Gravitational Field Intensity and Gravitational potential Fue to a Spherical Shell:The gravitational field intensity and gravitational potential due to a spiritual shell of radius R and mass M at a point distant r from the centre of the shell is given as follows: Gravitational Field Intensity and Gravitational Potential Due To A Spherical Shell.At a point outside the shell i.e. r > a${E_{outside}} = - \dfrac{{GM}}{{{r^2}}}$, ${V_{outside}} = - \dfrac{{GM}}{r}$At a point on the surface of the shell i.e. r = a${E_{surface}} = - \dfrac{{GM}}{{{a^2}}}$,${V_{surface}} = - \dfrac{{GM}}{a}$At a point inside the shell i.e. r ${E_{inside}} = 0$, ${V_{inside}} = - \dfrac{{GM}}{a}$Gravitational Field Intensity and Gravitational Potential Due To A Solid Sphere:The gravitational field intensity and gravitational potential duty a solid sphere of radius R and mass M at a distance r from the centre of the sphere is given as follows: Gravitational Field Intensity and Gravitational Potential Due to a Solid SphereAt a point outside the sphere, i.e. r > a${E_{outside}} = - \dfrac{{GM}}{{{r^2}}}$ ${V_{outside}} = - \dfrac{{GM}}{r}$At a point on the surface of the sphere, i e. r = a${E_{surface}} = - \dfrac{{GM}}{{{a^2}}}$ ${V_{surface}} = - \dfrac{{GM}}{a}$At a point inside the sphere, i.e. r ${E_{inside}} = - \dfrac{{GMr}}{{{a^3}}}$, ${V_{inside}} = - \dfrac{{GM\left( {3{a^2}
2025-04-23A blurring operation. Theoretically, it is important that the mask does not introduce high-frequency correlations between the two half maps. Only building blurred masks helps reduce the chance of this happening.Open the volume in ChimeraX. This example uses the results of a non-uniform refinement. For all commands in this example, the base volume is volume #1.Blur the volume using a Gaussian filter: volume gaussian #1 sDev 2. Increasing the value for sDev will make the map more blurry. This command creates a new, blurred volume. The blurred base volume is volume #2.Step 2: Create copies of the blurred volumeSince the volume eraser tool directly modifies the volume it operates on, you must create another copy of the blurred volume if you plan on creating a mask for Particle subtraction.Copy the map with volume copy #2Step 3: Erase the region outside the desired maskIn this step, we will erase the regions outside the mask using the Volume Eraser tool. This tool creates a sphere and allows you to erase everything either inside or outside the sphere. There is no undo function for this tool, so be careful when erasing volumes. You can create copies of the volume as you go if the process is long and complicated using volume copy as above.Open the volume eraser tool: Right Mouse ribbon menu > Erase. You should see a sphere appear. Holding down right-click and dragging your mouse moves the sphere. Erasing inside or outside the sphere is accomplished with the buttons in the
2025-04-07