How 2d Screens Render 3d Objects

Gehendraraj Pyakurel

How 2d Screens Render 3d ObjectsComputers have evolved at a tremendous pace in the last century, but the reason computers are a worldwide phenomenon today is because of the combination of different aspects developed by different people at different times. The computation, rendering, hardware, software and other aspects of the modern day computer were developed as a result of the combined effort of many people at once, But even among all the features that have been developed, computer rendering is the sole thing that transcended computers from fancy calculators to personal computers used by billions of people worldwide.Before we continue, we must understand what “rendering” and “rasterization” mean. Rendering is putting the 3d object in our 2d screen, rasterization is making perfect mathematical equations into pixelated images. Our computer screen is a 2d plane of pixels that draw images, texts and other recognizable glyphs and symbols that allow us to interact with, rendering is a special process that makes 3d objects appear to render in a 2d plane, for a better understanding, we can take our own Eyes as a reference too! Have you ever noticed that a great painting is practically indistinguishable from something you'd actually see? This is because our eyes see the 3d world in 2d, the well drawn art just mimics the same thing onto another 2d plane! So, trying to render 3d objects into a 2d screen is the same as discovering how our eyes work (mathematically!) P(x, y, z) ● /| / | / | / | / | / | / | / |👁 O───────────────┼────────┼────────────→ z <--- f ---> Screen Pz ● P'(x', y', f)The most important formula that makes 3d rendering possible comes from a simple derivation, and is the fundamental to any graphics rendering is the projection formula. A detailed explanation is given below extracted from a recent rasterization project of mine“ This very simple function is what makes 3D graphics possible. the way it works is that it takes a 3D point and projects it onto a 2D plane. When you look around you, you are looking at a 2D projection of a 3D world. you might've noticed how putting objects further away from you makes them smaller, they approximate to what we call a vanishing point, around (0,0) from any plane, that includes our eyes. let us consider the distance from our eyes to the screen as f or focal length. our eyes are at )(0,0,0) and the screen is at S(0,0,f) Let us assume a point P(x,y,z) and our eyes are looking at it. The vector joining our eyes to the point to the point is simply P-O. but, before reaching our eyes when the rays intersect the screen, they will intersect at a point P'(x',y',f). The vector P-O represents a distance of D units; D=P-O Now let us assume a line that slowly goes from P to O.the starting point would be Line=Point O, and the ending point would be initial point + the distance vector ..Making us reach the point P.But assuming the line to a function we deduce that the line; L(t)=O+t*D where t is a small incremented value that goes from 0 to 1, and D is the distance vector. Now, finally: When the point increments and reaches z=f; L(t)=O+t*D L(t)=(0,0,0)+t*(x,y,z) [hence; (x,y,z)-(0,0,0)=(x,y,z)] L(t)=(t*x,t*y,t*z) Since the line reaches (t*x,t*y,t*z) at z=f, we can say; L(t)=P' P'(x',y',f)=(t*x,t*y,t*z) Equating Corresponding components, we get; t*z=f t=f/z substituting t in the other components, we get; x'=t*x=(f/z)*x y'=t*y=(f/z)*y which is the final formula, but since we can assume f=1 units which can be whatever distance from user to screen, we can simplify it to; x'=x/z y'=y/z for further clarification, we can think of it like this. If our head is constantly in place then, the projection of the 3d object is accurate to scale of the this.canvas/screen/this and our eyes, the shape retains but we perceive it differently. Human error is not inducive for perspective. a good analogy is; if we make an eye and want it to stare the user we make it look at (0,0) if the player moves to the right, the eye will still look at (0,0) but the player will perceive it as if the eye is looking at the left, that is the users fault not ours and doesn't need fixing!“ Other optimizations are required for a good renderer, but the barebones of all formulae run on this exact formula!(To see a live demonstration check out: https://arkaive19.is-a.dev/roobiks)

Science and Technology

Krishna Chaudhary

Science and Technology As we know science is built on investigations concerning existent stuff around us. Likewise, technology is applied science. Technology is the means by which we can get many things in a few seconds.” We are living in the 21st century. At this moment, in 2026, scientists and engineers are developing remarkable new gadgets to help us live, work and remain healthy. Scientists make theories and hypotheses and make some shocking things which we can not believe or understand. The simplest method to learn is to ask how it works and what the reasoning is behind that technology. Below is a simple explanation of some of the more important ones. Custom cancer vaccines Now doctors can develop specific vaccines for just one person. Cancer. They look at the patient’s cancer and make a vaccine from the mRNA. ( Same goes for COVID resources). These vaccines are targeting cancer and they are helping the patient to live longer. This is such a huge step towards curing cancer because it allows people to live happier lives. Better and cheaper batteries. In everyday life we all use lithium batteries in phones and electric automobiles, but they are expensive and consume rare elements. There are many different types of batteries used in cars and phones. Sodium-ion batteries are employed, which are safer and easier to build. This will assist. Produce electric cars at a lower cost and facilitate the storage of solar and wind energy. This is good news for us and for our environment. smarter computers and artificial intelligence Quantum computers are growing more powerful. They can handle incredibly hard tasks, such as creating machines that are faster than regular ones. This method reduces sophisticated programming languages into simpler, more understandable forms. Every second AI is responsible for countless innovations that help foster a more scientific world that embraces technology. Scientists do experiments all the time. Scientists build robots and teach us about robotics and coding. The advantages and benefits of science and technology are significant. Science makes it easy to learn about nature and surroundings. Technology produces unexpected ideas on different logical principles It makes our life easier to keep us current with scientific advancements and allows us to live. . It saves our time and helps us to face problems. Robots and AI lessen the activities of many women making ladies feel comfortable in the daily lives of visitors. Conclusion: Sparks of science and technology are part of our life. Science and technology help us to solve issues and to explain things that are not clear.. Sparks is science and technology. This is the present time of the universe.

Unheard

Sameeha Nepal

UnheardIt was the middle of the night.I could feel those nasty hands crawling over me.I couldn't even shout or say, "No."What makes it worse is that it's someone I know.I see it. I see it happening once more.Thinking about it leaves me sore.It's funny how people think it's not a big deal,When they don't know how I feel.It's not once, not twice, not even thrice.Who's going to listen to all my past cries?Cries of disgust, cries of guilt,All slowly breaking the person I've built.Once again, men proving why they are hated.I question what society has created.You question the girl for being harassed.What about the man who did it at last?Teach your sons before the world must.Raise them with respect, fairness, and trust.Change your mindset; break the old mold,Because excuses are growing old.A "no" is a "no"—hear the sound.That's where respect is truly found.Never make a woman live in fear;The time to change is finally here.

मेरो क्युट साथी

Baikuntha Gautam

मेरो क्युट साथीसुप्रभात, मेरो क्युट साथी,सूर्यकाे किरणझैँ चम्किलो तिम्रो साथ।तिमी हाँस्दा झलमल्ल बन्छ संसार,मुस्कानले भरिन्छ हरेक बिहान ।बगैँचाका फूलको सुगन्धझैँ,तिम्रो सौन्दर्यले मन छुन्छ सधैँ ।चन्द्रमाको उज्यालोभन्दा पनि प्यारो,तिम्रो मुहार लाग्छ सबैभन्दा प्यारो।तिम्रा नयनले मन चोरेका छन्,मायाका सपना कोरेका छन् ।मन्द हावासँग लहरिने तिम्रो चाल,मनमा बजाउँछ प्रेमको मधुर ताल ।चाँदनी रातको मिठो सन्देश,ताराहरूले गाएका छन् विशेष ।तिम्रो एउटै मुस्कान देख्न देखेर,जीवनभरका सबै दुःख बिर्सिएँ ।तारा र चन्द्र नाचिरहेझैँ लाग्छ,तिम्रो छायाले मन मोहित बनाउँछ।तिम्रो कोमल स्वर मधुर गीत,तिमी नै हौ संसारकै प्रिय सृष्टि।मेरो क्युट साथी, तिम्रै नाममा,यो सानो कविता प्रेमिल भावमा।सधैँ मुस्कुराइरहे, सधैँ रमाइरहे,साथी तिमी सधैँ बाँची रहे सधैँ हाँसिरहे ।

प्रविधि

Sebastian Tiwari

प्रविधिआजको युग प्रविधिको युग हो। विज्ञान र प्रविधिले मानव जीवनलाई सहज, छिटो र प्रभावकारी बनाएको छ। शिक्षा, स्वास्थ्य, कृषि, व्यापार, सञ्चार, यातायात र सरकारी सेवामा प्रविधिको प्रयोग व्यापक रूपमा भइरहेको छ। प्रविधि मानव जीवनको अभिन्न अङ्ग बनेको छ, केवल विलासिताको साधन मात्र नभएर मानव जीवनको अनिवार्य अङ्ग र अस्तित्वको बलियो आधार बनिसकेको छ। बिहान आँखा खोलेर मोबाइलको स्क्रिन हेरेदेखि राति नसुत्दासम्म हामी प्रत्यक्ष रूपमा प्रविधिको सञ्जालभित्रै घेरिएका हुन्छौँ। प्रविधिले संसारलाई यसरी बाँधिदिएको छ कि याेबिनाको आधुनिक जीवनको परिकल्पना गर्नु पनि असम्भव जस्तै देखिन्छ।शिक्षाको क्षेत्रमा प्रविधिले ठुलो परिवर्तन ल्याएको छ। पहिले पुस्तक र कक्षाकोठामा मात्र सीमित शिक्षा अहिले इन्टरनेट, कम्प्युटर र मोबाइलमार्फत जहाँसुकैबाट प्राप्त गर्न सकिन्छ। विद्यार्थीहरूले अनलाइन कक्षा लिन, अध्ययन सामग्री डाउनलोड गर्न तथा विश्वका प्रतिष्ठित शैक्षिक संस्थाका पाठहरू अध्ययन गर्न सक्छन्। यसले सिकाइलाई अझ प्रभावकारी बनाएको छ।स्वास्थ्य क्षेत्रमा पनि प्रविधिको महत्त्वपूर्ण योगदान रहेको छ। आधुनिक उपकरणहरूको प्रयोगबाट रोगको पहिचान छिटो र सही रूपमा गर्न सकिन्छ । टेलिमेडिसिन सेवाका कारण दुर्गम स्थानका बिरामीले पनि विशेषज्ञ चिकित्सकसँग परामर्श लिन सक्ने भएका छन्। नयाँ औषधि, शल्यक्रिया प्रविधि तथा अनुसन्धानले मानिसको आयु र जीवनस्तर सुधार गर्न सहयोग पुर्‍याएको छ। खोप र नयाँ औषधिको विकासमा आधुनिक प्रविधिको ठुलो योगदान छ। अस्पतालमा बिरामीको विवरण डिजिटल रूपमा राख्ने प्रणालीले सेवा छिटो र व्यवस्थित बनाएको छ।कृषि क्षेत्रमा आधुनिक मेसिन, उन्नत बीउ, सिँचाइ प्रणाली तथा मौसमसम्बन्धी जानकारीले उत्पादन वृद्धि गर्न मद्दत गरेको छ। व्यापार र उद्योगमा डिजिटल भुक्तानी, अनलाइन किनमेल तथा स्वचालित प्रणालीको प्रयोगले समय र खर्च दुवै बचाएको छ। सरकारी सेवाहरू पनि क्रमशः डिजिटल बन्दै गएका छन्, जसले नागरिकलाई छिटो र पारदर्शी सेवा प्राप्त गर्न सहयोग गरेको छ। ड्रोनको प्रयोगबाट बालीको अवस्था निरीक्षण र विषादी छर्कन सजिलो भएको छ। अनलाइन बजारमार्फत किसानले आफ्ना उत्पादन प्रत्यक्ष रूपमा बिक्री गर्न सक्ने भएका छन्।नेपालमा पनि पछिल्ला वर्षहरूमा प्रविधिको विकास तीव्र रूपमा भइरहेको छ । अनलाइन बैंकिङ, डिजिटल वालेट, अनलाइन शिक्षा तथा सूचना प्रविधिमा आधारित सेवाहरू विस्तार हुँदै गएका छन् तर अझै पनि ग्रामीण क्षेत्रमा इन्टरनेटको पहुँच, गुणस्तरीय पूर्वाधार र प्राविधिक जनशक्तिको अभाव चुनौतीका रूपमा रहेका छन्। यी समस्याको समाधान गर्दै प्रविधिलाई सबै नागरिकको पहुँचमा पुर्‍याउन आवश्यक छ।एक सिक्काका दुई पाटा भए झैँ प्रविधिको यो उज्यालो पाटोका पछाडि केही अँध्यारा चुनौतीहरू पनि लुकेका छन्। प्रविधिको अत्यधिक र अविवेकी प्रयोगले समाजमा नयाँ र जटिल किसिमका समस्याहरू जन्माएका छन् । साइबर अपराध, डाटा चोरी, अनलाइन ठगी र सामाजिक सञ्जालमार्फत फैलाइने अफवाह एवं घृणा आजको विश्वकै लागि ठुलो सुरक्षा चुनौती बनेको छ। यसको अर्को गम्भीर असर मानव स्वास्थ्य र सामाजिक संरचनामा परेको देखिन्छ। स्क्रिनमा धेरै समय बिताउनाले मानिसहरूमा आँखाको समस्या, अनिन्द्रा, शारीरिक निष्क्रियता र मानसिक तनाव बढ्दै गएका छन्। आफ्नै परिवारसँग कुरा गर्ने फुर्सद हुँदैन, जसले गर्दा हाम्रा सामाजिक मूल्यमान्यता र व्यावहारिक सम्बन्धहरू कमजोर बन्दै गएका छन्।अन्त्यमा, प्रविधि आफैँमा राम्रो वा नराम्रो हुँदैन, यसको प्रभाव हामीले कसरी प्रयोग गर्छौँ भन्ने कुरामा निर्भर हुन्छ। यदि प्रविधिलाई ज्ञान, अनुशासन र जिम्मेवारीका साथ प्रयोग गरियो भने यसले समाज, राष्ट्र र सम्पूर्ण मानव जातिको समृद्धिमा ठुलो योगदान पुर्‍याउन सक्छ। त्यसैले प्रविधिको सदुपयोग गर्दै यसको नकारात्मक प्रभावलाई कम गर्नु आजको समयको प्रमुख आवश्यकता हो।

My Favorite Food

Sambodhi Gurung

My Favorite FoodMy favorite food is pizza. Pizza is one of the most popular foods in the world. It was first made in Italy. Long ago, it was a simple and affordable meal for ordinary people. Later, it became famous after Queen Margherita of Italy enjoyed a special pizza made for her. Today, people all over the world love eating pizza.Pizza is made with a flat, round dough topped with tomato sauce, cheese, and different ingredients such as chicken, ham, mushrooms, or vegetables. There are many types of pizza, and each one has its own delicious taste.I have eaten pizza from many different places. My favorite is the chicken pizza from Pokhara Pizza House. I enjoy eating pizza with my family and friends because it is tasty and fun to share. Pizza is my favorite food, and I always look forward to eating it.

पुस्तक समीक्षाः ओडारको बत्ती

Abhinya Ghimire

पुस्तक समीक्षाः ओडारको बत्तीकथा परिचयः ओडारको बत्ती चित्रकथा हो । यस कथाको लेखक कविता बोहराज्यू हुनुहुन्छ। यस कथाका चित्रकार रवि बस्नेत ज्यू हुनुहुन्छ । यस कथाभित्र १५ वटा पृष्ठ सङ्ख्याहरू छन् । यस कथा खोजी प्रकाशनले प्रकाशनमा ल्याएको हो ।पात्रहरूः यस कथामा नौ जना पात्रहरू छन् । करुणा, बुबा, आमा, हजुरआमा, दिदी, माइजू, मामा, अन्जली र भिखम हुन् । यस कथाको मुख्य पात्र करुणा हुन् ।कथावस्तुः यस कथामा एउटी करुणा हुन्छिन्। उनले साँझमा जहिले पारीतिर बत्ती बलेको देख्थिन्। तर खाना खाएपछि उनले फेरि हेर्दा बत्ती निभेको हुन्छ। उनले त्यो बत्तीको धेरै जिज्ञासा गर्छिन् । त्यो के होला ? कसले बालेको होला ? यस बारेमा उनले आमाबुबालाई सोधिन् तर आमाबुबाले उनलाई कराउनु पो भयो । त्यसपछि उनी पल्लाघरको मामालाई गएर सोधिन् तर कसैले उत्तर दिएनन् । भोलिपल्ट उनी फेरि मामाघरमा दिदीसँग खेल्न गइन्। दिदीलाई त्यहाँ डाँडातिर जान मन लागेको थियो तर करुणा डराइन् । दिदीले साथीहरू बटुलेर जाने भन्ने कुरा गर्नुभयो । त्यसपछि सबैजना साथीहरू मिलेर त्यहाँ गए । एकछिनपछि उनीहरू डाँडामा पुगे । डाँडामा गुफा र बुढी मान्छे देखे । उनीहरू बुढी आइमाईतिर गए । त्यहाँ हजुरआमाले करुणालाई नातिनी भनेर बोलाउनुभयो । करुणा छक्क परिन् । करुणाकी दिदीले भन्नुभयो “उहाँ तिम्रो हजुरआमा हो” करुणा फेरि छक्क परेर रुन थालिन् । त्यसपछि हजुरआमाले सबैलाई मकैको रोटी खान दिनुभयो । त्यसपछि हजुरआमालाई करुणाको घरमा मिलेर लगे । करुणाको आमाबुबाले नचिने झैँ गरी नाटक गर्नुभयो । सबैजना कराउन थाले। त्यसपछि सबैजना अँगालो बाँधेर खुसी भए ।निष्कर्षः यस कथाबाट हामीले एकअर्कालाई सहयोग गर्नुपर्छ, सम्मान गर्नुपर्छ। हजुरबा हजुरआमाको साथ बालबालिकालाई प्यारो हुन्छ भन्ने कुराको शिक्षा पाउँछाैँ ।