📚 GCSE Cambridge Art: Formula & Theorem Quick Reference Handbook | GCSE 剑桥艺术：公式定理速查手册
This quick-reference handbook gathers the essential ‘formulas’, rules and principles that underpin successful GCSE Cambridge Art & Design work. Use these proven relationships for colour mixing, perspective, composition, figure drawing and technique to build confidence and accuracy in your practical portfolio.
这本速查手册汇集了支撑 GCSE 剑桥艺术与设计作品的必备‘公式’、规则与原理。运用这些经过验证的色彩混合、透视、构图、人体素描和技法关系，帮助你在实践作品集中建立信心与精确度。
1. The Formula for Mixing Colours: Primary, Secondary & Tertiary | 色彩混合公式：原色、间色与复色
Understanding subtractive colour mixing is fundamental for painting. The three primary hues cannot be created by mixing; they are the building blocks from which all other colours emerge.
理解减色法混合是绘画的基础。三原色不能由混合产生；它们是生成所有其他颜色的基石。
| Red + Yellow = Orange | 红 + 黄 = 橙 |
| Blue + Yellow = Green | 蓝 + 黄 = 绿 |
| Red + Blue = Violet | 红 + 蓝 = 紫 |
Tertiary colours are produced by mixing a primary with its neighbouring secondary. The naming formula is Primary-Secondary, e.g. Red-Orange, Yellow-Green, Blue-Violet.
复色由一种原色与其相邻的间色混合产生。命名公式为原色-间色，例如红橙、黄绿、蓝紫。
| Red + Orange = Red-Orange | 红 + 橙 = 红橙 |
| Yellow + Orange = Yellow-Orange | 黄 + 橙 = 黄橙 |
| Yellow + Green = Yellow-Green | 黄 + 绿 = 黄绿 |
| Blue + Green = Blue-Green | 蓝 + 绿 = 蓝绿 |
| Blue + Violet = Blue-Violet | 蓝 + 紫 = 蓝紫 |
| Red + Violet = Red-Violet | 红 + 紫 = 红紫 |
2. Complementary Colour Pairs and the After-Image Rule | 互补色对与残像规则
Complementary colours sit opposite each other on the colour wheel. When placed side by side, they create maximum contrast and visual vibration; when mixed, they neutralise each other towards brown or grey.
互补色在色轮上彼此相对。并列时产生最大对比和视觉震动；混合时彼此中和，趋向棕色或灰色。
Red ↔ Green
红 ↔ 绿
Blue ↔ Orange
蓝 ↔ 橙
Yellow ↔ Purple
黄 ↔ 紫
A useful painting rule: to darken a hue without using black, add a small amount of its complement. This yields a more natural, luminous shadow.
一条实用的绘画规则：想要调暗一个色相而不用黑色，就加入少量其补色。这样能获得更自然、透亮的暗部。
3. One-Point Perspective: Depth Formula | 一点透视：深度公式
One-point perspective uses a single vanishing point on the horizon line. All receding parallel lines (orthogonals) converge at that point, creating the illusion of depth on a flat surface.
一点透视使用地平线上的单一消失点。所有后退的平行线（正交线）都汇聚于该点，在平面上营造深度幻觉。
Depth Illusion = Vanishing Point + Horizon Line + Converging Orthogonal Lines
深度幻觉 = 消失点 + 地平线 + 汇聚的正交线
Object Size ∝ 1 / Distance from Viewer
物体大小 ∝ 1 / 与观者的距离
Place the horizon line at eye level. Objects above the horizon appear below eye level in the picture plane; objects below it appear above. The closer an object is to the vanishing point, the smaller and more compressed it becomes.
将地平线置于视平高度。地平线以上的物体在画面中显得低于视平线，以下的物体显得高于视平线。物体离消失点越近，就显得越小、越压缩。
4. Two-Point Perspective: Dual Vanishing Points | 两点透视：双消失点法则
Two-point perspective engages two vanishing points on the same horizon line, typically used when a corner of an object faces the viewer. This formula generates more dynamic and realistic representations of 3D space.
两点透视使用同一地平线上的两个消失点，通常用于物体的一个角正对观者。该公式能产生更富动感和真实感的三维空间表现。
Two-Point Realism = Horizon Line + Left Vanishing Point + Right Vanishing Point
两点真实感 = 地平线 + 左侧消失点 + 右侧消失点
All vertical edges remain vertical in two-point perspective. The left set of horizontal edges converges to the left vanishing point, the right set to the right vanishing point. The vanishing points should be far apart to avoid distortion.
两点透视中所有垂直边缘保持垂直。左侧的水平边缘汇聚于左消失点，右侧的汇聚于右消失点。消失点应相距较远以避免变形。
5. Rule of Thirds: Dynamic Composition | 三分法：动态构图公式
The rule of thirds divides the picture plane into a 3×3 grid. Placing key subjects or focal points along these lines or at their intersections creates a balanced yet energetic composition.
三分法将画面划分为 3×3 的网格。将关键主体或焦点放在这些线或交点上，可形成均衡而又充满活力的构图。
Grid = 2 horizontal lines + 2 vertical lines → 4 power points
网格 = 2 条水平线 + 2 条垂直线 → 4 个兴趣点
Subjects placed on the ‘power points’ naturally attract the eye and avoid the static feel of centred placement. This formula applies to landscapes, portraits and still life.
将主体置于‘兴趣点’上能自然吸引视线，并避免中心放置的呆板感。该公式适用于风景、肖像和静物。
6. Golden Ratio and Fibonacci Spiral for Composition | 黄金比例与斐波那契螺旋构图
The golden ratio (φ ≈ 1.618) has been used for centuries to achieve harmonious proportion. The Fibonacci spiral derived from it guides the viewer’s eye through a composition in a natural, pleasing flow.
黄金比例（φ ≈ 1.618）数百年来被用于实现和谐的比例。由它派生出的斐波那契螺旋能引导观者视线以自然宜人的方式流转于画面。
φ = (1 + √5) / 2 ≈ 1.618
φ = (1 + √5) / 2 ≈ 1.618
Fibonacci Spiral Curve: 1, 1, 2, 3, 5, 8, 13…
斐波那契螺旋曲线：1, 1, 2, 3, 5, 8, 13…
Position the compositional anchor within the tight coil of the spiral and allow secondary elements to radiate outward along its expanding arms. This creates an unforced, organic sense of movement.
将构图锚点置于螺旋紧密的内圈，让次要元素沿着螺旋外扩的臂部向外辐射。这能营造出一种不刻意的、有机的运动感。
7. Figure Drawing Proportions: The 8-Head Canon | 人体素描比例：八头身准则
In classical and academic figure drawing, the average adult human body is approximately 7.5 to 8 heads tall. This modular measurement system helps artists maintain accurate proportions from any angle.
在古典与学院派人体素描中，成年人体身高约为 7.5 至 8 个头长。这套模块化测量系统帮助艺术家从任何角度保持准确比例。
Total Body Height = 8 × Head Height
身长 = 8 × 头高
| 0 – 1 heads: Top of head to chin | 0–1 头：头顶至下巴 |
| 1 – 2 heads: Chin to nipples | 1–2 头：下巴至乳头 |
| 2 – 3 heads: Nipples to navel | 2–3 头：乳头至肚脐 |
| 3 – 4 heads: Navel to crotch | 3–4 头：肚脐至胯部 |
| 4 – 5 heads: Crotch to mid-thigh | 4–5 头：胯部至大腿中段 |
| 5 – 6 heads: Mid-thigh to bottom of knee | 5–6 头：大腿中段至膝盖底 |
| 6 – 7 heads: Knee to mid-calf | 6–7 头：膝盖至小腿中段 |
| 7 – 8 heads: Mid-calf to heel | 7–8 头：小腿中段至脚跟 |
Use the head length as a unit of measurement with the thumb-and-pencil sighting technique to establish accurate life proportions quickly.
用头长作为测量单位，结合铅笔拇指瞄准法，即可快速建立准确的人体比例。
8. Value and Shading Scale: 9-Step Gradient | 明度与调子：九级灰度公式
A systematic value scale is essential for rendering form, light and shadow. The 9-step scale moves from pure white (1) to pure black (9), with mid-grey at step 5. Mastering this gradient allows convincing tonal modelling.
系统化的明度标尺对表现形体、光与影至关重要。九级标度从纯白（1）过渡到纯黑（9），中灰位于第 5 级。掌握这组渐变能呈现出真实感十足的黑白灰塑造。
| 1 – White (highlight) | 1 – 白（高光） |
| 2 – Pale grey | 2 – 浅灰 |
| 3 – Light grey | 3 – 亮灰 |
| 4 – Mid-light | 4 – 中浅灰 |
| 5 – Mid-grey (50% black) | 5 – 中灰（50% 黑） |
| 6 – Mid-dark | 6 – 中深灰
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