Low eye, high eye眼睛低，眼睛高
Your eye rises from 0.6 m to 2.2 m. The eye-level line and the vanishing point rise with it the whole way.
眼睛從 0.6 公尺升到 2.2 公尺。視平線和消失點一路跟著升高。
Art · Unit 2 · Lesson 5 · 美術 單元二 第五課
How Do You Draw a Room on Flat Paper?怎麼在平面上畫出一個房間？
Look down a hallway through a window and move your eye up, down, and sideways. Watch the vanishing point follow you, then find it yourself in five line drawings.
透過一扇窗戶看一條走廊，把眼睛往上、往下、往旁邊移動，看消失點怎麼跟著你走；再到五張線稿裡自己把它找出來。
Big idea · 一句話看懂
Lines that are parallel and run away from you look as if they meet at one point, the vanishing point. That point sits on a level line at the height of your eyes, the eye-level line. Things of the same size are drawn smaller the farther away they are. With those three ideas you can draw a room on a flat sheet of paper.
彼此平行、而且離你越來越遠的線，看起來會在一個點相交，那就是消失點。消失點落在一條和眼睛一樣高的水平線上，叫做視平線。一樣大的東西，離得越遠就畫得越小。有了這三件事，就能在一張平平的紙上畫出一個房間。
3D Model · 3D 模型
A Hallway Seen Through a Window 透過一扇窗戶看走廊
Imagine a window 4 meters wide and 3 meters tall standing at the mouth of a hallway. Your eye is 3 meters in front of it. Drag the picture, or use the sliders, to move your eye. The window never moves. The dotted line marks your eye level and the gold dot marks the vanishing point. Switch to Line drawing to see the same view as lines on paper, and turn on the two posts to compare near and far.
想像走廊口立著一扇寬 4 公尺、高 3 公尺的窗戶，你的眼睛在窗戶前面 3 公尺的地方。拖動畫面或用滑桿，移動的是你的眼睛；窗戶不會動。點狀的線標出視平線，金色的圓點標出消失點。切換到「紙上的線稿」，看同一個畫面變成紙上的線；打開兩根柱子，比較近和遠。
Drag the picture to move your eye · 拖動畫面，移動你的眼睛
This 3D model needs WebGL, which this browser does not support. The sliders on the right still work and still give the position of the horizon and the vanishing point, and the two activities below draw the same hallway without WebGL.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；右邊的滑桿照樣能用，也照樣寫出視平線與消失點的位置；下面兩個小互動不需要 WebGL，畫的是同一條走廊。
- The gold dot: the vanishing point, straight in front of your eye
金色圓點：消失點，就在眼睛的正前方 - The dotted line: the eye-level line (the horizon line of the picture)
點狀的線：視平線（這張畫的地平線） - The dashed gold lines: the edges of the hallway, continued to the vanishing point
金色虛線：走廊的邊線，一路延長到消失點
The hallway is 4 m wide, 3 m tall, and 18 m long, with floor tiles 1 m square. The three eye heights (0.6 m, 1.2 m, 2.2 m) are round numbers chosen for the model.
走廊寬 4 公尺、高 3 公尺、長 18 公尺，地磚每塊 1 公尺見方。三種眼睛高度（0.6、1.2、2.2 公尺）是替模型選的整數，不是量出來的。
What this model leaves out 這個模型簡化了什麼
- The model uses one eye that stays still. You have two eyes, and they are always moving. Linear perspective is a system for drawing from a single fixed viewpoint. It is close to what we see, and it is not the same thing.模型用的是一隻不動的眼睛。你有兩隻眼睛，而且它們一直在動。線性透視是一套「從單一固定視點來畫」的方法；它很接近我們看到的樣子，但不等於視覺本身。
- Every line going into the distance here is level and points straight ahead, so there is one vanishing point. Turn a box at an angle and it needs two. Lines that slope up or down, such as a roof or a ramp, meet above or below the eye-level line.這裡每一條往遠處延伸的線都是水平的，而且朝正前方，所以只有一個消失點。把一個箱子轉個角度，就需要兩個。往上或往下斜的線（例如屋頂、斜坡），則在視平線的上方或下方相交。
- A perspective picture is exactly right from one spot only: the place where the eye was. From anywhere else it is a little off, though it usually still looks fine.一張透視圖，只有從一個位置看才完全正確：就是當初眼睛所在的地方。從別的地方看都有一點偏差，不過通常看起來還是可以。
- The walls and floor are flat colors with no light and shade. Lesson 3 showed what shading adds, and Lesson 6 looks at other ways painters show distance.牆和地板都是平塗的顏色，沒有明暗。明暗能加上什麼，第三課講過了；畫家表現遠近的其他方法，留到第六課。
So test it in a real hallway. Classroom Activity 1 shows how, with nothing more than a window pane and a marker.所以請到真的走廊去驗證；做法在課堂活動一，只需要一片透明的板子和一支筆。
Hallway and line drawings made for this lesson. The perspective math is in shared code that later lessons reuse, and it is covered by automatic tests. · 走廊與線稿為本課自行繪製；透視的計算放在之後的課共用的程式裡，並有自動測試。
Reading · 英文閱讀
5
Unit 5: How Do You Draw a Room on Flat Paper?
Look at a photograph of a straight railway track, or stand at one end of a long hallway at school. The two sides are the same distance apart all the way along. You know that. Yet they look as if they are closing in on each other, and far away they seem to touch. Your paper is flat, and a room is not. The trick of drawing a room is to copy this closing-in exactly.
看一張筆直鐵軌的照片，或站在學校長長的走廊的一頭。兩邊之間的距離，從頭到尾都一樣寬，這你是知道的。可是它們看起來卻越靠越近，到了很遠的地方好像碰在一起。紙是平的，房間不是。要畫出一個房間，訣竅就是把這種「越靠越近」原原本本地畫下來。
Artists call the system linear perspective. Its first rule is about parallel lines. Lines that run away from you, side by side, look as if they meet at a single point. That point is called the vanishing point. The sides of a road and the rails of a railway are the examples everyone knows. In a hallway the edges of the floor and the ceiling do the same thing, and so do the tops of the doors.
藝術家把這套方法叫做線性透視。第一條規則和平行線有關：並排著、離你越來越遠的線，看起來會在同一個點相交。這個點叫做消失點。馬路的兩邊和鐵路的兩條軌道，是大家都知道的例子。在走廊裡，地板和天花板的邊線也是這樣，每一扇門的上緣也是。
Where is the vanishing point? It is on a level line at the height of your own eyes. Artists call it the eye-level line or the horizon line. Crouch down and it drops. Climb on a chair and it rises with you. Things below your eye level, like the floor, have lines that slope up toward it. Things above your eye level, like the ceiling, have lines that slope down. Step to the left and the vanishing point moves left as well. It is always straight in front of you.
消失點在哪裡？在一條和你的眼睛一樣高的水平線上。藝術家把這條線叫做視平線，也叫地平線。蹲下來，它就降低；站到椅子上，它跟著你升高。比視平線低的東西，例如地板，它的線往上斜向視平線；比視平線高的東西，例如天花板，它的線往下斜。往左跨一步，消失點也跟著往左。它永遠在你的正前方。
The second rule is about size. Things look smaller the farther away they are. Move a post twice as far from your eye and it looks half as tall. Move it three times as far and it looks one third as tall. The post has not changed. It simply takes up a smaller angle in your view. Perspective lets a painter work out exactly how big to draw each thing for its distance.
第二條規則和大小有關：東西離得越遠，看起來越小。把一根柱子移到離眼睛兩倍遠的地方，它看起來只有一半高；三倍遠，就只有三分之一高。柱子並沒有變，只是它在你視野裡占的角度變小了。有了透視，畫家就能算出每一樣東西在那個距離該畫多大。
People in Florence, Italy, worked this system out about six hundred years ago. It is generally accepted that the architect Filippo Brunelleschi made a series of experiments between 1415 and 1420, drawing the city's buildings in correct perspective. His painted panels are lost. In 1435 Leon Battista Alberti wrote the method down in a book called On Painting. A few years earlier the painter Masaccio had already used it for a wall painting of the Trinity in a church in Florence.
大約六百年前，義大利佛羅倫斯的人把這套方法弄清楚了。一般認為，建築師布魯內萊斯基在 1415 到 1420 年之間做了一連串實驗，用正確的透視畫出城裡的建築。他畫的那幾塊板子已經失傳。1435 年，阿爾伯蒂把這個方法寫進一本叫《論繪畫》的書。在這之前幾年，畫家馬薩喬已經用它在佛羅倫斯的一座教堂裡畫了〈聖三位一體〉壁畫。
Linear perspective is one way of drawing space. It is not the only way. It assumes one eye that never moves, while you have two eyes that are always moving. Chinese landscape painters chose a different path. Their pictures do not keep to a single fixed viewpoint, and the eye travels through them as if on a walk. Lesson 15 goes there. For now, find the eye level, find the vanishing point, and aim your lines at it.
線性透視是畫出空間的一種方法，不是唯一的方法。它假設只有一隻不動的眼睛，而你有兩隻一直在動的眼睛。中國的山水畫家走的是另一條路：他們的畫不拘泥於單一固定的視點，眼睛可以在畫裡像散步一樣移動。那是第十五課的事。現在，先找出視平線，找出消失點，再讓你的線對準它。
Read aloud · 課文朗讀
Questions · 閱讀理解
You are drawing a hallway. Where on your paper should the vanishing point go, and what decides it?
It goes on the eye-level line, straight in front of where your eye is. If you are low, the line is low on the paper. If you stand to one side, the point moves to that side.
Two posts are the same height. One is 5 m from your eye and the other is 15 m away. How do their heights compare on your drawing?
The far post is three times as far away, so it is drawn one third as tall as the near one.
Why is a perspective drawing not exactly the same as what a person sees?
Linear perspective assumes one eye that stays in one place. People look with two eyes that keep moving. The drawing is a close and very useful approximation.
Words & Phrases · 生字及片語
perspective(n.)透視（法）With perspective, a flat drawing can look deep.有了透視，平面的圖也能看起來有深度。parallel(adj.)平行的The two rails of a track are parallel.鐵路的兩條軌道是平行的。vanishing point(n.)消失點The edges of the hallway meet at the vanishing point.走廊的邊線在消失點相交。eye level(n.)視平線；眼睛的高度The vanishing point is at your eye level.消失點和你的眼睛一樣高。horizon(n.)地平線The sun went down below the horizon.太陽落到地平線下面去了。distance(n.)距離；遠處The road seems to narrow in the distance.馬路在遠處看起來變窄了。converge(v.)匯聚；靠攏The lines converge on a single point.這些線往同一個點靠攏。viewpoint(n.)視點；觀看的位置Move your viewpoint and the picture changes.改變觀看的位置，畫面就跟著變。
Quick Check · 小測驗
1. What do we call the point where lines going into the distance seem to meet?
2. Where is the eye-level line in a perspective drawing?
3. You climb on a chair. What happens to the vanishing point in your view of the hallway?
4. A post is moved twice as far from your eye. How tall does it look now?
5. Which statement about linear perspective is true?
Try It in the Model · 在模型裡試試
Four things to try 四件值得試的事
Then try it yourself. Where must your eye be for the floor to fill most of the picture? Can you put the vanishing point exactly on the handle of the door at the far end?
然後自己動手試試。眼睛要在哪裡，地板才會占掉大半個畫面？你能把消失點剛好放在盡頭那扇門的門把上嗎？
Step to the side往旁邊走
You walk from the left wall to the right. The vanishing point crosses the picture with you, always straight ahead.
你從左邊的牆走到右邊。消失點跟著你橫越畫面，永遠在正前方。
The hallway as a drawing把走廊變成線稿
The same view becomes black lines on paper. Follow any edge that goes into the distance and it leads to the gold dot.
同一個畫面變成紙上的黑線。順著任何一條往遠處去的邊線走，都會走到金色的圓點。
Same height, different size一樣高，畫出來不一樣大
Two posts of equal height stand near and far. The far one is three times as far away and one third as tall on the picture.
兩根一樣高的柱子，一近一遠。遠的那一根是三倍遠，在畫面上只有三分之一高。
Game · 小遊戲
Where Is the Vanishing Point? 消失點在哪裡？
Five line drawings: hallways, railway tracks, and a street. In each one, click the spot where the lines that go into the distance would meet. You can move your mark with the arrow buttons. Press Check to see how close you were. The drawing then continues its own lines to the true point.
五張線稿：走廊、鐵軌和一條街。每一張都點出那些往遠處延伸的線會相交的地方；可以用方向按鈕移動你標的位置。按「對答案」看看差多少，圖上會把它自己的線一路延長到真正的消失點。
Picture 1 of 5 · 第 1 張（共 5 張）
Found · 找到的張數 0 / 0
A tip from drawing class: lay a ruler along two of the receding lines, one after the other, and see where they cross.素描課的小技巧：拿一把尺，先後貼著兩條往遠處去的線，看它們在哪裡交叉。
Measure It · 量量看
Which Post Is Taller? 哪一根比較高？
Two posts stand in the hallway. Slide post B nearer or farther and read the numbers. In the room the two posts are always the same height. On the picture they are not. Then draw the lines through their tops and their feet, and see where those lines go.
走廊裡立著兩根柱子。把柱子 B 滑近或滑遠，讀讀數字。在走廊裡，兩根柱子永遠一樣高；在畫面上卻不是。再畫出通過頂端和底端的線，看看這些線通到哪裡。
This is the rule from the reading: an object looks N times smaller when it is N times as far from the eye.這就是課文裡的規則：一樣東西離眼睛 N 倍遠，看起來就是 N 分之一大。
Stories Behind the Vanishing Point · 消失點背後的故事
A lost panel, a book, a wall in Florence, and mountains seen while walking 一塊失傳的板子、一本書、佛羅倫斯的一面牆，和邊走邊看的山
Four short stories about how people learned to put space on a flat surface.
關於人怎麼把空間放到平面上的四個小故事。
Florence, about 1415–1420 · 佛羅倫斯，約 1415–1420 年
Brunelleschi's lost panels布魯內萊斯基失傳的板子
Filippo Brunelleschi was an architect. The Metropolitan Museum's timeline says he demonstrated his system of linear perspective in two experimental panels showing buildings in Florence, the Baptistery and the Palazzo della Signoria. Both panels are lost. Later writers reported that, in about 1420, he had people look at a painted panel through a small hole. Because the panels are gone, nobody can check today how exact they were.
布魯內萊斯基是一位建築師。大都會博物館的年表說，他用兩塊實驗用的板子示範了線性透視，畫的是佛羅倫斯的洗禮堂和領主宮。兩塊板子都已經失傳。後來的作者記載，大約在 1420 年，他讓人透過一個小孔去看畫好的板子。板子不在了，所以今天沒有人能檢查它們到底有多準。
1435 · 一四三五年
Alberti writes it down阿爾伯蒂把它寫下來
Leon Battista Alberti wrote On Painting in Latin in 1435, and an Italian version followed in 1436, addressed to Brunelleschi. The National Gallery in London says the single-point system was invented by Brunelleschi and set out by Alberti in this book. Its glossary describes the picture plane as a transparent division between the space inside the painting and the real space where the viewer stands. The window in this lesson's model is that idea.
阿爾伯蒂在 1435 年用拉丁文寫了《論繪畫》，1436 年又有義大利文版，書前的獻詞是寫給布魯內萊斯基的。倫敦國家美術館說，單點透視由布魯內萊斯基發明，由阿爾伯蒂在這本書裡整理成文。它的詞彙表把「畫面」形容成一道透明的分界：一邊是畫裡的空間，一邊是觀看的人所站的真實空間。這一課模型裡的那扇窗戶，就是這個想法。
About 1425–1428 · 約 1425–1428 年
Masaccio's Trinity馬薩喬的〈聖三位一體〉
In the church of Santa Maria Novella in Florence, Masaccio painted the Trinity on a flat wall so that it looks like a deep chapel with a curved ceiling. The Met's timeline says it applies Brunelleschi's ideas of linear perspective to painting, and the vanishing point is at the viewer's eye level. It is an early and famous example. It is not perfect: studies of its geometry have found errors, as in most paintings of that century.
在佛羅倫斯的新聖母教堂，馬薩喬在一面平平的牆上畫了〈聖三位一體〉，看起來卻像一間有拱頂的深深的小禮拜堂。大都會博物館的年表說，這件作品把布魯內萊斯基的線性透視用到了繪畫上；它的消失點就在觀看者眼睛的高度。這是早期很有名的例子，但並不完美：研究它的幾何的人發現了誤差，那個世紀的大多數畫作也是如此。
Chinese Landscape · 山水畫
A viewpoint that moves會移動的視點
Taiwan's Ministry of Education dictionary says that Chinese painting commonly arranges its scenes with a moving viewpoint and does not keep to a single focus point of perspective. An education encyclopedia adds that Chinese landscapes use many points where Western landscapes use one, so one picture can show height, depth, and level distance together. It is a different answer to the same question, and Lesson 15 returns to it.
教育部辭典說，中國畫「普遍以移動視點的方式取景布局，視野寬廣，不拘泥於焦點透視」。《教育大辭書》補充：中國山水畫不像西洋風景畫採單點透視，而採多點透視或散點透視，所以一個畫面裡往往同時有高遠、深遠、平遠三種空間。這是對同一個問題的另一種回答；第十五課會再回來談。
In the Curriculum · 對應課綱
Where this lesson fits 這一課對應的課綱
The visual arts curriculum does not use the word perspective. These are the closest entries, and their links to this lesson are our reading of them.
視覺藝術課綱的條文沒有出現「透視」。下面是最接近的條目；它們和這一課的連結，是本教材的解讀。
視 E-Ⅱ-1藝術領域・視覺藝術（國小三、四年級） · Arts, visual arts (grades 3–4)
色彩感知、造形與空間的探索。
Exploring space is the subject of this unit, and perspective is one way to draw it.「空間的探索」正是這個單元的主題；透視是畫出空間的一種方法。
視 E-Ⅱ-3藝術領域・視覺藝術（國小三、四年級） · Arts, visual arts (grades 3–4)
點線面創作體驗、平面與立體創作、聯想創作。
A point, lines aimed at it, and the planes between them: a room in perspective is built from exactly these.一個點、對準它的線、線與線之間的面：透視裡的房間就是用這些組成的。
視 E-Ⅳ-2藝術領域・視覺藝術（國中） · Arts, visual arts (grades 7–9)
平面、立體及複合媒材的表現技法。
Linear perspective is a technique for showing a solid space on a flat surface.線性透視是在平面上表現立體空間的一種技法。
INe-Ⅱ-6自然科學領域（國小三、四年級） · Science (grades 3–4)
光線以直線前進，反射時有一定的方向。
The model works because light travels in straight lines from each point of the hallway to the eye.模型之所以成立，是因為光從走廊的每一點沿直線走到眼睛。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思The vanishing point is always in the middle of the paper.消失點一定在紙的正中間。
✓ Fact · 事實It is straight in front of the eye, at eye level. If the viewer is low, high, or off to one side, the point moves there. In the model you can put it almost anywhere.消失點在眼睛的正前方、和眼睛一樣高的地方。觀看的人位置偏低、偏高或偏向一邊，它就跟著移過去。在模型裡，你幾乎可以把它放在任何地方。
✗ Myth · 迷思Things far away are drawn smaller because they really are smaller.遠處的東西畫得比較小，是因為它們真的比較小。
✓ Fact · 事實Their size has not changed. A thing that is farther away takes up a smaller angle in your view, so it is drawn smaller. Two posts of the same height prove it.它們的大小並沒有變。東西離得遠，在視野裡占的角度就小，所以畫得小。兩根一樣高的柱子就能證明這件事。
✗ Myth · 迷思Linear perspective shows the world exactly as our eyes see it.線性透視畫出來的，就是眼睛看到的樣子。
✓ Fact · 事實It is a geometric system for one eye that does not move. We see with two eyes in constant motion. The picture is an approximation, and it is exactly right from one viewing spot only.它是替「一隻不動的眼睛」設計的幾何方法。我們是用兩隻不停移動的眼睛在看。畫出來的是近似，而且只有從一個觀看位置看才完全正確。
✗ Myth · 迷思A picture without a vanishing point is drawn wrong.沒有消失點的畫，就是畫錯了。
✓ Fact · 事實Linear perspective is one way of showing space. Chinese landscape painting uses a moving viewpoint, and painters in the Netherlands made convincing rooms by eye, without the Italian system.線性透視是表現空間的一種方法。中國山水畫用的是移動的視點；尼德蘭的畫家不靠義大利那套方法，憑觀察也畫出了令人信服的房間。
Remember It · 記憶口訣
Perspective in a sentence 一句話記住透視
Far lines meet遠去的線會相交
Parallel lines that run away from you aim at one vanishing point.
離你遠去的平行線，都對準同一個消失點。
Eye level is the horizon視平線就是眼睛的高度
Crouch and it drops. Climb and it rises.
蹲下它就降低，爬高它就升高。
Twice as far, half as tall兩倍遠，一半高
Three times as far, one third as tall.
三倍遠，就是三分之一高。
Below slopes up, above slopes down低的往上斜，高的往下斜
Floor lines climb to the eye level. Ceiling lines come down to it.
地板的線往上斜向視平線；天花板的線往下斜向它。
Before You Start · 動手之前
Hallways, rulers, and windows 走廊、尺和窗戶
- Never stand on or near a real railway track or in a road to look at perspective. Use a hallway, a sidewalk, or a photograph.絕對不要為了看透視而站到真的鐵軌上、鐵軌旁或馬路中間。請用走廊、人行道或照片。
- Ask an adult before you stand on a chair, and have someone hold it steady. Crouching is always safe.要站到椅子上之前先問大人，並請人扶穩。蹲下來看永遠是安全的。
- If you trace on a window, use a marker that wipes off, ask first, and do not lean on the glass.要在窗戶上描的話，用擦得掉的筆，先問過大人，而且不要靠在玻璃上。
- Rest your eyes: ten minutes after every thirty minutes of close work.讓眼睛休息：用眼每 30 分鐘休息 10 分鐘。
Classroom Activity 1 · 課堂活動一
Trace a Hallway on a Window 把走廊描在一扇「窗戶」上
You need · 準備材料
- A clear plastic sheet or folder, about the size of a notebook一片透明的塑膠片或資料夾，大約筆記本大小
- A marker that wipes off, and a ruler一支擦得掉的筆，和一把尺
- A long hallway, or a room with a tiled floor一條長走廊，或一間鋪了地磚的教室
- A partner一位同伴
Steps · 步驟
- Stand at one end of the hallway. Your partner holds the clear sheet upright at arm's length in front of your face.站在走廊的一頭。請同伴把透明片立起來，舉在你面前一隻手臂遠的地方。
- Close one eye and keep your head still. Trace the edges of the floor and the ceiling as you see them through the sheet.閉上一隻眼睛，頭不要動。把透過透明片看到的地板邊線和天花板邊線描下來。
- Lay the sheet on a desk. Use the ruler to continue your lines until they cross. Mark the crossing.把透明片放到桌上，用尺把這些線延長到交叉為止，標出交點。
- Hold the sheet up again in the same place. What part of the hallway is behind your mark? How high is it compared with your eye?把透明片舉回原來的位置。交點後面是走廊的哪裡？和你的眼睛比起來，它有多高？
- Crouch and trace again in another color. Compare the two crossings, and then compare them with the model on this page.蹲下來，換一種顏色再描一次。比較兩個交點，再和這一頁的模型比一比。
Your lines may not cross at one neat point. A head that moves a little, or a second eye that opens, is enough to spoil it. That is what the model means by one eye that stays still.
你的線不一定會剛好交在一個點上。頭稍微動一下，或另一隻眼睛睜開了，就足以把它弄亂。這正是模型說的「一隻不動的眼睛」的意思。
Classroom Activity 2 · 課堂活動二
Draw a Hallway in One-Point Perspective 用一點透視畫一條走廊
You need · 準備材料
- White paper, a sharp pencil, an eraser, and a ruler白紙、削尖的鉛筆、橡皮擦和尺
- This page, with the model set to Line drawing這一頁，模型設在「紙上的線稿」
Steps · 步驟
- Draw a light level line across the paper. This is your eye level. Put a dot on it for the vanishing point.在紙上輕輕畫一條水平線，這是你的視平線。在線上點一個點，當作消失點。
- Draw a small rectangle around the dot. This is the wall at the far end of the hallway.繞著那個點畫一個小長方形。這是走廊盡頭的牆。
- Lay the ruler from the vanishing point through each corner of the rectangle and draw outward to the edge of the paper. These four lines are the edges of the floor and the ceiling.把尺從消失點貼著長方形的每一個角，往外畫到紙的邊緣。這四條線就是地板和天花板的邊線。
- Add two doors on the side walls. Their tops and bottoms aim at the vanishing point, and their sides stand straight up.在兩邊的牆上各加一扇門。門的上緣和下緣對準消失點，門的兩側是垂直的。
- Set the model's eye to match your drawing and compare. Then draw the hallway again with the eye level much lower.把模型裡的眼睛調到和你的圖一樣的位置，比較一下。然後把視平線畫低很多，再畫一次。
Keep the first lines light so you can erase them. In one-point perspective only the lines that go into the distance are slanted. Lines that run across the picture stay level, and lines that stand up stay upright.
一開始的線畫輕一點，才擦得掉。在一點透視裡，只有往遠處去的線是斜的；橫過畫面的線保持水平，直立的線保持垂直。
Go Further · 延伸閱讀
Lines, light, and what comes next 線、光，以及下一課
Art · Lesson 4 · 美術・第四課What Can a Line Say?一條線可以說什麼？Perspective is built from lines. That lesson has a drawing pad where you can practice aiming them.透視是用線搭起來的。那一課有一塊畫板，可以練習讓線對準目標。Go to the lesson · 前往這一課 →How Things Work · Lesson 12 · 萬物原理・第十二課How Does a Camera Take a Picture?相機怎麼拍下照片？A camera also gathers light through one small opening onto a flat surface, so photographs show the same vanishing points.相機同樣讓光穿過一個小小的開口、落在一個平面上，所以照片裡也有同樣的消失點。Go to the lesson · 前往這一課 →Art · Lesson 6 · 美術・第六課How Do Painters Show Near and Far?畫家怎麼畫出遠和近？Overlap, size, position, and the way far hills turn pale and blue: the other tools for showing distance.重疊、大小、位置，還有遠山越來越淡、越來越藍：表現遠近的其他工具。Go to the lesson · 前往這一課 →
Sources · 資料出處
Names, dates, numbers, and quotations on this page were checked against these sources (October 2026). The positions of the vanishing point and the sizes on the picture are computed by the page itself and covered by automatic tests; the sizes of the hallway are chosen for the model · 本頁的人名、年代、數字與引文依下列資料查證（2026 年 10 月）；消失點的位置與畫面上的大小由頁面自己計算，並有自動測試；走廊的尺寸是替模型選的
- Linear perspective: receding parallel lines appear to converge on a single point on the horizon線性透視：往遠處的平行線看起來在地平線上的一點相交The National Gallery, London, glossary: Linear perspective ↗
- The single-point system was invented by Brunelleschi and codified by Alberti in On Painting (1435); Netherlandish painters worked empirically單點透視由布魯內萊斯基發明、阿爾伯蒂在《論繪畫》（1435）整理成文；尼德蘭畫家憑觀察作畫The National Gallery, London, glossary: Perspective ↗
- Vanishing point: the position at which all receding parallel lines meet消失點：所有往遠處的平行線相交的位置The National Gallery, London, glossary: Vanishing point ↗
- Picture plane: the transparent division between the space in the painting and the viewer's real space畫面：畫中空間與觀看者真實空間之間那道透明的分界The National Gallery, London, glossary: Picture plane ↗
- Roads and railway lines as examples; things look smaller the farther away they are; a single fixed viewpoint, and two eyes in constant motion馬路與鐵路的例子；東西越遠看起來越小；單一固定的視點，以及兩隻不停移動的眼睛Tate, Art Terms: Perspective ↗
- An object looks N times smaller when moved N times farther from the eye; Brunelleschi's experiments between 1415 and 1420; the demonstration through a hole in about 1420; the panel is lost; errors in fifteenth-century constructions; exactness from one vantage point東西離眼睛 N 倍遠，看起來就是 N 分之一大；布魯內萊斯基 1415–1420 年的實驗；約 1420 年透過小孔的示範；板子已失傳；十五世紀作品的幾何誤差；只有從一個位置看才完全正確Wikipedia “Perspective (graphical)” ↗
- The horizon line represents the eye level of the observer; lines below it angle up and lines above it slope down地平線代表觀看者眼睛的高度；比它低的線往上斜，比它高的線往下斜Wikipedia “Vanishing point” ↗
- Brunelleschi's two experimental panels (now lost); Masaccio's Trinity applies his theories of linear perspective to painting布魯內萊斯基的兩塊實驗板（已失傳）；馬薩喬的〈聖三位一體〉把他的線性透視用到繪畫上The Metropolitan Museum of Art, Heilbrunn Timeline of Art History ↗
- On Painting: written in Latin in 1435《論繪畫》：1435 年以拉丁文寫成Wikipedia “De pictura” ↗
- The Italian version of 1436, addressed to Brunelleschi1436 年的義大利文版，獻給布魯內萊斯基Wikipedia “Leon Battista Alberti” ↗
- Masaccio's Holy Trinity: dates and the vanishing point at the viewer's eye level馬薩喬〈聖三位一體〉：年代，以及位於觀看者眼睛高度的消失點Wikipedia “Holy Trinity (Masaccio)” ↗
- The dictionary entry for 中國畫: a moving viewpoint, not bound to a single focus of perspective「中國畫」：普遍以移動視點的方式取景布局，不拘泥於焦點透視教育百科〈中國畫〉（教育部辭典） ↗
- Three distances: Chinese landscapes use many points of view where Western landscapes use one三遠：中國山水畫不像西洋風景畫採單點透視，而採多點透視或散點透視教育百科〈三遠〉（教育大辭書） ↗
- The dictionary entry for 透視「透視」：從假設的透明平面視察物象，即用線條或色彩在平面上表現立體空間的方法教育百科〈透視〉（教育部辭典） ↗
- Standard Chinese terms: linear perspective, vanishing point, eye level, horizon line, one-point perspective學術名詞：線性透視、消失點、視平線、地平線、一點透視國家教育研究院 樂詞網 ↗
- Visual arts learning content: 視 E-Ⅱ-1, 視 E-Ⅱ-3, 視 E-Ⅳ-2; science: INe-Ⅱ-6視覺藝術學習內容：視 E-Ⅱ-1、視 E-Ⅱ-3、視 E-Ⅳ-2；自然科學：INe-Ⅱ-6十二年國教課綱 藝術領域（教育部，2018） ↗
- Eye rest: ten minutes after every thirty minutes of close work護眼：用眼每 30 分鐘休息 10 分鐘衛生福利部國民健康署 ↗