📚 Year 8 AQA Art: Formulas and Theorems Quick Reference Handbook | Year 8 AQA 艺术：公式定理速查手册
Art might seem like a subject driven by intuition and feeling, yet it has its own set of 'formulas' and 'theorems' that help you master colour, perspective, proportion, and composition. This quick-reference handbook turns those creative principles into simple, memorable rules you can use in every sketch and painting. Whether you are mixing colours, building a landscape with depth, or planning a portrait, these fundamental formulas will make your work stronger and more confident.
艺术虽然看似随性与直觉，但它同样拥有一套独特的“公式”和“定理”，帮助你牢牢掌握色彩、透视、比例与构图。这本速查手册将这些创作原理转化为简单好记的法则，让你在每一次速写和绘画中都能随时调用。无论你在调配颜色、营造有深度的风景，还是规划一幅肖像，这些基础公式都会让你的作品更扎实、更有底气。
1. Colour Mixing Formulas (Subtractive) | 颜料混合公式（减色法）
When working with paint, ink or pencil, you use subtractive colour mixing. The primary colours are cyan, magenta and yellow. By mixing two primaries in equal parts, you get a secondary colour. The basic formulas are:
在使用颜料、墨水或彩铅时，我们采用的是减色混合。三原色为青、品红和黄。将两种原色等量混合，便得到一种间色。基础公式如下：
Cyan + Magenta = Blue (often called purple-violet range)
Magenta + Yellow = Red (scarlet to orange-red)
Yellow + Cyan = Green
青 + 品红 = 蓝（常表现为紫罗兰色系）
品红 + 黄 = 红（猩红至橙红色系）
黄 + 青 = 绿
en. To darken a colour, add its complement in small amounts, not black straight away. To lighten, add white or water.
要调出复色，可将一种原色与相邻的间色混合。如黄 + 绿 = 黄绿。想要把颜色变暗，可以少量加入它的补色，而不是直接用黑色。想要变亮，则可加入白色或用水稀释。
2. Complementary Colours and Visual Vibration | 互补色与视觉震颤
Complementary colours sit opposite each other on the colour wheel. When placed side by side, they create maximum contrast and seem to 'vibrate'. The three main complementary pairs are red–green, blue–orange, and yellow–purple. Use this formula to make focal points pop: place a small amount of a warm colour against a cool complementary background.
互补色在色相环上彼此相对。当它们并排放置时，会产生最强对比并仿佛在“震颤”。三对主要的互补关系是红—绿、蓝—橙和黄—紫。善用这一定式可以让焦点跃然纸上：将少量暖色放在冷色的互补背景上即可。
Mixing two complements in equal proportion produces a neutral grey or brown. This is the painter's shortcut to natural shadows without using black. Add just a touch of orange to blue, and you get a deep, natural shadow tone.
将两种互补色等比例混合，会生成中性灰或棕色。这是画家不依赖黑色也能画出自然阴影的捷径。往蓝色中加入少许橙色，便能得到深沉自然的暗部色调。
3. Colour Harmony Formulas (Triadic, Analogous, Monochromatic) | 色彩和谐公式（三角、类似、单色）
To create a balanced colour scheme, artists rely on simple geometric formulas on the colour wheel. A triadic harmony uses three colours equally spaced, such as orange, green and violet. This formula gives a lively yet balanced palette.
为了创造色彩平衡，艺术家依赖色相环上的简单几何公式。三角和谐使用的是三种等距分布的颜色，如橙、绿、紫。这种配方既活泼又均衡。
An analogous formula selects 3–5 colours that sit next to each other on the wheel, for example, yellow, yellow-green and green. This creates a calm, unified look ideal for landscapes. A monochromatic scheme uses only one hue with different tints (hue + white) and shades (hue + black). It is the simplest harmony formula and always works.
类似色公式选取色相环上相邻的3至5种颜色，例如黄、黄绿、绿。它能营造安静统一的视觉效果，特别适合风景画。单色方案则只用一种色相，搭配不同的明度与暗度（加白或加黑）。这是最简单的和谐公式，永远不会出错。
4. Perspective Rules: One-Point Perspective Formula | 透视法则：一点透视基本公式
One-point perspective uses a single vanishing point on the horizon line. All lines that go away from the viewer (orthogonal lines) converge at this point. The formula is: first draw the horizon line, place one vanishing point, then draw the front face of the object. Connect the corners of that face to the vanishing point to create depth.
一点透视采用地平线上的单一消失点。所有向画面深处退去的线条（正交线）都汇聚于此。公式是：先画出地平线，放置一个消失点，再画出物体的正面。将正面的各个角与消失点相连，便能生成深度。
For a room interior, draw the back wall first, then connect its corners to the vanishing point to build floor, ceiling and side walls. This gives an immediate sense of realistic space, like standing in a corridor.
绘制室内空间时，先画出后墙，再将其四个角与消失点连接，从而构建地面、天花板和两侧墙壁。这能立刻带来真实的空间感，仿佛站在一条走廊里。
5. Two-Point Perspective and Depth Formula | 两点透视与深度公式
When you look at the corner of a building, you see two sets of receding lines, each going to its own vanishing point on the horizon line. In two-point perspective, vertical lines stay vertical. Only horizontal edges recede to the left vanishing point (LVP) or right vanishing point (RVP).
当你看向建筑物的转角时，会看到两组后退的线条，各自奔向地平线上左右两个消失点。在两点透视中，所有竖线保持垂直，只有水平方向的棱边分别向左消失点或右消失点后退。
To construct a box, draw a vertical edge first. From its top and bottom, draw lines to LVP and to RVP. Decide the length of each side with another vertical edge, then join the corners. This formula is essential for drawing streets, furniture, and any object seen from an angle.
绘制一个方体时，先画一条垂直棱边，从它的上下两端向左右消失点连线。用另外两条竖线决定左右侧面的长度，再连接各个角。这一定式对画出街道、家具和任何斜角观察的物体都至关重要。
6. Proportions of the Human Body: The 8-Head Canon | 人体比例法则：八头身定理
unit of measurement. The key divisions are: chin to nipple line = 2 heads; nipple line to navel = 1 head; navel to crotch = 1 head; crotch to mid-thigh = 1.5 heads; mid-thigh to knee = 1.5 heads; knee to heel = 2 heads. The halfway point of the whole figure is just below the crotch.
在人物绘画中，成年人的身高大约等于8个头高，俗称八头身。头部本身被用作测量单位。关键的分界是：下巴到乳头连线 = 2头；乳头连线到肚脐 = 1头；肚脐到胯部 = 1头；胯部到大腿中部 = 1.5头；大腿中部到膝盖 = 1.5头；膝盖到脚跟 = 2头。整个人体的二分之一处刚好在胯部下缘。
For a Year 8 artist, simplifying to 7.5 or 7 heads can also work for slightly shorter figures. Always compare proportions with a real-life model or reference, but use this formula to check your sketch.
对八年级学生而言，使用7.5或7头身来表现稍矮小的人物也完全可行。始终要结合真人模特或参考图来比较比例，但可以用这个公式检查你的速写。
7. Golden Ratio in Composition | 黄金分割与构图
The golden ratio, approximately 1 : 1.618, appears in nature, architecture and art. In a rectangle, if you divide its longer side by 1.618, you get a spiralling grid that leads the eye to the focal area. You can use this formula to place the main subject of your painting at the golden ratio lines or intersections.
黄金比例大约为 1 : 1.618，广泛存在于自然界、建筑和艺术中。在一个矩形内，将长边除以1.618，你会得到一条螺旋式引导视线的网格。运用这一公式，可将画面主体安放在黄金分割线或交叉点上。
Many master paintings, such as those by Leonardo da Vinci, subtly follow the golden ratio to create balanced, naturally pleasing compositions. Even a simple rule: the smaller part is to the larger as the larger is to the whole, can guide where you put the horizon or a tree.
许多大师画作，如达·芬奇的作品，都暗藏黄金比例，以达到均衡且自然的悦目效果。即便只用一句话——较小部分与较大部分之比等于较大部分与整体之比——也能指导你地平线或树的位置。
8. Rule of Thirds | 三分法则
The rule of thirds is a simplified, widely used compositional formula. Imagine your canvas divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines. The four intersection points are the strongest places to position your main subject.
三分法则是简化且广泛运用的构图公式。设想画面被两条等距横线和两条等距竖线分成九个等份，那四个交叉点就是放置主体的最佳位置。
Landscape painters often place the horizon along the top or bottom third line, never in the exact middle, to avoid a static look. A portrait artist might align the eyes with the top horizontal line. This formula instantly lifts a composition from dull to dynamic.
风景画家常将地平线放在上或下三分之一线处，而从不放在正中间，以避免呆板。肖像画则可让眼睛对齐上方的横线。这一定式能让构图瞬间从平淡变得生动。
9. Light, Shadow and Shading Formula | 光影与阴影公式
Every solid form has a light source. The shading formula identifies five zones: highlight, mid-tone, core shadow, reflected light and cast shadow. Start by deciding the direction of your light. The side directly facing the light gets the highlight, the turning point from light to dark is the core shadow, and a little bounced light from the ground creates reflected light on the shadow side. The cast shadow is darkest nearest the object.
任何立体形态都有光源。光影公式可归纳为五个区域：高光、中间调、明暗交界线、反光和投影。先确定光线方向。正对光源的面是高光；由明转暗的转折处是明暗交界线；地面反弹的一点光线会在暗部产生反光。投影在物体紧挨处最暗。
shadow but dark near the base; reflected light = mid-tone between core shadow and cast shadow. Practise with a sphere, cylinder and cube to embed this logic.
按照这套公式：高光 = 纸张的留白或最亮调子；明暗交界线 = 形体自身最暗处；投影 = 略淡于交界线，但底部附近较深；反光 = 交界线与投影之间的中等调子。通过球体、圆柱体和方体反复练习，内化这套逻辑。
10. Texture and Mark-Making Formulas | 纹理与笔触公式
Texture is suggested by the pattern, density and pressure of your marks. A rough texture formula: use short, erratic lines or stippled dots close together. For smooth surfaces, use long, even, closely spaced parallel lines with consistent pressure. To create a gradient from dark to light, gradually increase the space between lines or dots.
纹理可通过笔触的走向、密度和力度来表现。粗糙质感公式：使用短促而不规则的线条，或密集的点。光滑表面则采用均匀的、间距紧密的平行长线条，力度保持一致。要想营造从深到浅的渐变，则逐渐拉大线条或点之间的间隔。
| Texture | Mark-Making Formula |
| Wood grain | Long wavy lines with small knots |
| Fur | Overlapping short strokes following growth direction |
| Glass | Sharp, high-contrast reflections; smooth blending |
| Stone | Irregular dots, dashes, and cross-hatching |
纹理 | 笔触公式
木纹: 长波浪线加上小结点
毛发: 沿生长方向重叠的短排线
玻璃: 锐利的高对比反射；光滑的渐变混合
石头: 不规则的点、短线和交叉排线
11. Tonal Value Formula for Depth | 调子深浅营造空间公式
Atmospheric perspective uses changes in tonal value, detail and colour temperature to suggest depth. The formula is: objects in the foreground have the darkest darks, richest colours and sharpest details. As objects recede into the distance, they become lighter in tone, bluer or greyer, and less detailed. This mimics the effect of air and moisture between the viewer and the far-away scene.
空气透视法通过调子深浅、细节和色温变化来表现纵深感。公式是：前景物体拥有最深的暗部、最饱和的颜色和最清晰的细节；随着物体向远处退去，明度变亮、色彩偏蓝灰，细节也减弱。这模拟了空气与雾气在观察者与远景之间的效果。
Apply this in a landscape: a tree up close is shown with dark browns and crisp leaves; the same tree on a distant hill is a pale, blue-grey silhouette. This value shift formula is one of the most powerful yet simple ways to create three-dimensional depth on a flat page.
在风景画中应用此法：近处的树用深棕色与清晰的叶片表现，远处山丘上的同一棵树则只是浅淡的蓝灰色剪影。这种调子变化公式，是在平面上创造三维空间感最强也最简单的手法之一。
12. Grid Enlargement Formula | 网格放大公式
When you need to transfer a small reference image to a larger canvas accurately, use the grid method. Draw a grid of equal squares on the reference and a proportionally larger grid of the same number of squares on the canvas. The formula: if the reference is 10 cm wide and you want a 30 cm wide drawing, the scale is 1 : 3. Each original 1 cm square becomes a 3 cm square on the larger paper.
当需要将一张小幅参考图精确放大到大幅画面上时，可使用网格法。在参考图上画等距方格，在画纸上按相同数量画出等比例放大的格子。公式是：若参考图宽10厘米，你想画出30厘米宽的作品，缩放比为1:3。原图每个1厘米方格在画纸上对应变成3厘米方格。
Copy the contents square by square. This formula helps maintain accurate proportions, especially for portraits, where the slightest shift can ruin a likeness. It is a practical, mathematical helper for any artist.
逐格复制内容。这一定式有助于保持准确的比例，尤其是在肖像画中，细微的偏移就可能破坏相似度。它是每位艺术家都实用的数学好帮手。
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