📚 Year 9 Cambridge Art: Formula & Theorem Quick Reference Handbook | 剑桥九年级艺术：公式定理速查手册
Art may seem like a world without formulas, but Cambridge Year 9 Art is built on visual principles that work like equations — once you learn them, every drawing, painting, and design becomes more controlled and expressive. This quick reference handbook collects the essential “formulas” and “theorems” of composition, colour, perspective, and proportion, giving you a toolkit you can return to again and again.
艺术看起来可能像是一个没有公式的世界，但剑桥九年级艺术恰恰建立在一系列像公式一样工作的视觉原理之上。一旦掌握了它们，每一幅素描、绘画和设计都会变得更有控制力，也更具表现力。这份速查手册收集了构图、色彩、透视和比例的基本“公式”与“定理”，为你提供一个可以反复查阅的工具箱。
1. Rule of Thirds Formula | 三分法公式
The Rule of Thirds states that an image should be divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines. Important compositional elements should be placed along these lines or at their intersections.
三分法指出，一幅画面应该用两条等距的水平线和两条等距的垂直线分成九个相等的部分。重要的构图元素应当放置在这些线条上或它们的交点处。
- Grid formula: divide width and height by 3 → place focal points at the four intersections.
- 网格公式：将宽度和高度分别除以3 → 将视觉焦点放在四个交叉点上。
Using this “formula” instantly strengthens the balance and interest of a landscape, still life, or portrait composition.
使用这个“公式”可以立刻增强风景、静物或肖像构图的平衡感和趣味性。
2. Golden Ratio Theorem (Phi, 1:1.618) | 黄金分割定理 (Φ，1:1.618)
The Golden Ratio describes a proportion where the ratio of a whole to its larger part is the same as the ratio of the larger part to the smaller part. In art, it is used to create harmonious divisions and spirals.
黄金分割描述了一种比例关系：整体与较大部分的比值等于较大部分与较小部分的比值。在艺术中，它被用来创造和谐的分割与螺旋形。
- Formula: a/b = (a+b)/a ≈ 1.618, where a > b.
- 公式：a/b = (a+b)/a ≈ 1.618, 其中 a > b。
- Application: create a golden rectangle by multiplying the short side by 1.618 to get the long side.
- 应用：将短边乘以1.618得到长边，即可得到一个黄金矩形。
Compositions based on the golden ratio often feel naturally pleasing to the eye and have been used from classical architecture to modern photography.
基于黄金分割的构图往往让人觉得自然而悦目，从古典建筑到现代摄影都被广泛使用。
3. Linear Perspective: One‑Point Perspective Equation | 线性透视：一点透视方程
In one‑point perspective, all receding parallel lines converge at a single vanishing point on the horizon line. The apparent size of an object diminishes as its distance from the viewer increases.
在一点透视中，所有向后延伸的平行线都会汇聚于地平线上的一个消失点。物体离观者越远，其表观尺寸越小。
- Vanishing point (VP) sits on the horizon line (HL) at eye level.
- 消失点（VP）位于视平线高度上的地平线（HL）上。
- n object’s height at distance d₁ is h, then at distance d₂ its height becomes h × (d₁/d₂).
- 深度缩放：如果一个物体在距离 d₁ 处的高度为 h，那么在距离 d₂ 处的高度变为 h × (d₁/d₂)。
Draw orthogonals (converging lines) from the object’s edges to the VP to construct solid-looking boxes and interiors.
从物体边缘向消失点画出正交线（汇聚线），即可构建具有立体感的方体和室内空间。
4. Two‑Point Perspective Setup | 两点透视设置
Two‑point perspective uses two vanishing points placed on the horizon line. Vertical lines remain vertical; horizontal lines in depth converge to either VP₁ or VP₂.
两点透视使用放置在地平线上的两个消失点。垂直线保持垂直；纵深方向的水平线分别汇聚于 VP₁ 或 VP₂。
- Rule: the angle between the two sets of receding lines contributes to the sense of space. Keep both VPs far apart to avoid distortion.
- 规则：两组后退线之间的角度决定空间感。保持两个消失点间距较大以避免变形。
- Drawing trick: start with the leading vertical edge, then project lines to VPs to build forms.
- 绘画技巧：从最前面的垂直棱边开始，然后向消失点引出线来构建立体。
This perspective formula is essential for drawing buildings, furniture, and any object seen from a corner view.
这种透视公式对于绘制建筑物、家具和任何从转角处观察的物体都至关重要。
5. Atmospheric Perspective Fade Rule | 空气透视衰减法则
Atmospheric perspective describes how distant objects appear lighter, bluer, and less detailed due to particles in the air. The “formula” is: contrast and saturation decrease with distance.
空气透视描述了远处的物体由于空气中的微粒而显得更亮、更蓝且细节更少。其“公式”为：对比度和饱和度随距离增加而降低。
- r shift: warmer, darker tones in the foreground → cooler, lighter tones in the background.
- 色彩变化：前景使用较暖、较暗的色调 → 背景使用较冷、较亮的色调。
- Detail gradient: sharp edges and textures only in the foreground; softer edges beyond.
- 细节梯度：清晰边缘和肌理只出现在前景；更远处边缘变柔和。
Apply this “fade rule” in landscapes to create a realistic depth illusion with very little effort.
在风景画中应用这条“衰减法则”，只需很少的功夫就能创造出逼真的深度错觉。
6. Colour Wheel Harmony Equations | 色轮和声方程
Colour harmony can be expressed as simple angle rules on a standard 12‑part colour wheel. These “equations” help you choose colour schemes that look balanced.
色彩和声可以表示为标准12色色轮上的简单角度规则。这些“方程”能帮助你选择看起来平衡的配色方案。
| Complementary | opposite colours (180° apart) | 互补色（相隔180°） |
| Analogous | colours next to each other (30°–60° span) | 邻近色（跨度30°–60°） |
| Triadic | three colours evenly spaced (120° apart) | 三色组（间隔120°） |
| Split‑complementary | one colour + the two colours next to its complement | 一种颜色＋其补色两侧的颜色 |
Treat these like recipes; start with a hue and use the angle rule to build the rest of the palette.
把这些当作配方来使用：选择一个色相，再用角度规则构建调色盘的其余部分。
7. Colour Mixing Subtractive Formula | 颜料混色减法公式
When mixing pigments, we work with subtractive colour. The basic primaries in painting are cyan, magenta, and yellow (plus black to darken). Mixing formulas help you predict results.
混合颜料时，我们使用的是减色法。绘画中的基本原色是青、品红和黄（加黑色来加深）。混色公式可以帮助你预测结果。
- Cyan + Magenta = Blue‑violet (absorbs red and green, reflects blue)
- 青色 + 品红 = 蓝紫色（吸收红和绿，反射蓝）
- Magenta + Yellow = Red‑orange (absorbs green and blue, reflects red)
- 品红 + 黄色 = 红橙色（吸收绿和蓝，反射红）
- Yellow + Cyan = Green (absorbs blue and red, reflects green)
- 黄色 + 青色 = 绿色（吸收蓝和红，反射绿）
To create tints, add white (reduces saturation). To create shades, add black or the colour’s complement (darkens and neutralises).
要制造浅色（tint），加入白色（降低饱和度）。要制造深色（shade），加入黑色或该颜色的互补色（加深并降低纯度）。
8. Value Scale Luminance Formula | 明度尺亮度公式
Value describes the lightness or darkness of a colour. A simple 9‑step value scale works as a reference “equation” for shading: 1 is pure white, 9 is pure black, and 5 is middle grey.
明度描述颜色的亮暗程度。一个简单的9级明度尺可以作为明暗表现的参考“方程”：1为纯白，9为纯黑，5为中灰。
- Relative luminance rule: any colour’s value can be checked by squinting — the colour should blend into the matching grey step.
- 相对亮度规则：任何颜色的明度可以通过眯眼观察来检查——该颜色应融入对应的灰色级中。
- Contrast formula: high contrast = at least 4 steps apart; low contrast = 1–2 steps apart.
- 对比度公式：高对比度 = 至少相差4个级别；低对比度 = 相差1–2个级别。
Using this value formula ensures your artwork reads clearly from any distance.
使用这个明度公式可以确保你的作品在任何距离观看都清晰可辨。
9. Human Figure Proportions: Idealised Canons | 人体比例：理想化准则
Classical figure drawing uses proportional canons — mathematical relationships between body parts. The most common for Year 9 is the 7½‑heads‑tall canon for an adult figure.
古典人体素描使用比例准则——身体各部分之间的数学关系。九年级最常用的是成年人体7½头身准则。
| Total height | 7½ heads (head length = top of skull to chin) | 总高度：7½个头长（头长从颅顶到下巴） |
| Shoulders | about 2 head‑lengths wide (males); slightly less (females) | 肩宽：约2个头长（男性）；稍窄（女性） |
| Elbow to wrist | ≈ 2 head‑lengths | 肘到腕：约2个头长 |
| Legs | from hip to floor ≈ 4 head‑lengths | 腿：从臀底到地约4个头长 |
These “formulas” give a reliable skeleton for gesture drawings and character design.
这些“公式”为速写和角色设计提供了可靠的骨架。
10. Symmetry and Balance Theorem | 对称与平衡定理
Visual balance is the theorem that the visual weight of elements should be distributed evenly around an implied central axis. Symmetry is the simplest case, but asymmetrical balance follows a more subtle “equation.”
视觉平衡定理指的是元素的视觉重量应该均匀地分布在一个隐含的中轴周围。对称是最简单的情形，但不对称平衡遵循更微妙的“算式”。
- Visual weight factors: larger, darker, more textured, and irregular shapes feel heavier.
- 视觉重量因素：较大、较暗、肌理更丰富和不规则的形状感觉更重。
- Balance equation: a small dark shape can balance a large light shape if positioned farther from the centre.
- 平衡方程：一个小而暗的形状，如果放置在离中心较远的位置，可以平衡一个较大而亮的形状。
Test balance by imagining a fulcrum under the composition — if the left and right sides feel equally “heavy,” the theorem is satisfied.
测试平衡的方法是想象构图下方有一个支点——如果左右两边感觉“重量”相等，定理就成立了。
11. Gestalt Principles: The Visual Grouping Formulas | 格式塔原理：视觉分组公式
Gestalt principles explain how the brain organises visual elements into groups. They act as rules of connection that you can use to guide the viewer’s eye.
格式塔原理解释了大脑如何将视觉元素组织成整体。它们好比是连接的规则，你可以用来引导观者的视线。
- Proximity formula: elements close together are seen as a group.
- 邻近公式：彼此靠近的元素被看作一个组。
- Similarity formula: elements sharing shape, colour, or size are grouped together.
- 相似公式：在形状、颜色或大小上相似的元素会被归为一组。
- Closure formula: the mind fills in missing parts to see a complete shape.
- 闭合公式：大脑会补全缺失的部分以看到一个完整形状。
These “formulas” are especially powerful in logo design, collage, and abstract composition.
这些“公式”在标志设计、拼贴画和抽象构图中尤其有效。
12. Emphasis and Focal Point Theorem | 强调与焦点定理
The focal point theorem states that every composition should have one dominant area that first captures the viewer’s attention. The surrounding elements must support this focal point without competing.
焦点定理指出，任何构图都应当有一个最先抓住观者注意力的主导区域。周围的元素必须支持这个焦点，而不能与之竞争。
- Contrast formula: the focal point breaks the prevailing pattern — by value, colour, size, or detail.
- 对比公式：焦点打破整体模式——通过明度、色彩、大小或细节来实现。
- Placement rule: position the focal point near one of the Rule of Thirds intersections for maximum impact.
- 位置规则：将焦点放置在三分法交叉点附近，以获得最大冲击力。
Designing around this theorem ensures the artwork has a clear message and a strong visual path.
围绕这一定理进行设计，能确保作品拥有明确的信息和强有力的视觉路径。
Published by TutorHao | Art Revision Series | aleveler.com
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