📚 IGCSE CAIE Art and Design: Formula and Principle Rapid Revision Handbook | IGCSE CAIE 艺术：公式定理速查手册
In IGCSE CAIE Art and Design, there are no chemical equations or physics laws, but there are reliable formulas: visual element equations, composition ratios, colour relationships and assessment-objective recipes. This rapid revision handbook turns the syllabus into a set of checkable principles you can use in your portfolio, sketchbook and timed examination.
在 IGCSE CAIE 艺术与设计中，没有化学方程式或物理定律，但有可靠的公式：视觉元素关系式、构图比例、色彩关系以及评分目标配方。本速查手册将考纲转化为一组可检查的原则，可用于作品集、速写本和限时考试。
1. Assessment Objective Formula | 评分目标公式
Every project is marked against four equal Assessment Objectives. Treat this as the master formula: AO1 Record + AO2 Explore + AO3 Develop + AO4 Present = 100%.
每个项目都按四个权重相同的评估目标评分。把这条当作总公式：AO1 记录 + AO2 探索 + AO3 发展 + AO4 呈现 = 100%。
AO1 means first-hand observation, sketches, photographs and notes. AO2 means experimenting with media and techniques. AO3 means refining ideas through analysis and artist links. AO4 means producing a final personal response.
AO1 指第一手观察、速写、照片和笔记；AO2 指尝试媒介与技术；AO3 指通过分析和艺术家关联完善想法；AO4 指完成最终的个性化回应。
Check evidence in your portfolio: every AO needs visible pages, annotation and practical outcomes. A common error is to show only final pieces without development, which weakens AO3.
在作品集中检查证据：每个 AO 都需要可见的页面、注释和实践成果。常见错误是只展示最终作品而没有发展过程，这会削弱 AO3 的表现。
| AO | Focus | Evidence | 中文重点 |
|---|---|---|---|
| AO1 | Record | Observation, photography, notes | 记录观察与想法 |
| AO2 | Explore | Media experiments, trials | 探索媒介与技术 |
| AO3 | Develop | Analysis, artist links, refinements | 发展想法并批判分析 |
| AO4 | Present | Final personal response | 呈现最终个性化成果 |
2. Visual Elements Formula | 视觉元素公式
The basic visual equation is: Subject + Line + Shape + Form + Tone + Texture + Pattern + Colour + Space = Visual Language.
基础视觉方程式：主题 + 线条 + 形状 + 形体 + 明暗 + 肌理 + 图案 + 色彩 + 空间 = 视觉语言。
Lines can be contour, gestural, implied or directional. Shapes are two-dimensional; forms are three-dimensional through tone and perspective. Texture is real or simulated. Space includes positive/negative space and depth.
线条可以是轮廓线、动态线、隐含线或方向线；形状是二维的，形体通过明暗和透视呈现三维；肌理有真实或模拟；空间包括正负形与深度。
If a drawing looks weak, run the element checklist: missing tone? weak negative space? repeated texture? unclear focal colour? This diagnostic formula saves time in timed conditions.
如果画面效果弱，就用元素清单检查：缺少明暗？负空间弱？肌理重复？焦点色彩不明确？这个诊断公式可在限时条件下节省时间。
3. Design Principles Formula | 设计原则公式
Visual impact = Balance + Contrast + Emphasis + Movement + Pattern + Rhythm + Unity + Proportion.
视觉冲击力 = 平衡 + 对比 + 强调 + 动势 + 图案 + 节奏 + 统一 + 比例。
Balance is symmetrical, asymmetrical or radial. Contrast can come from tone, colour, size, texture or idea. Emphasis is created by placing the focal point off-centre, through isolation, or with the highest contrast.
平衡有对称、不对称和放射式；对比可来自明暗、色彩、大小、肌理或观念；强调通过将焦点偏离中心、孤立主体或制造最高对比来实现。
Unity means all parts belong together; use a limited palette, repeated mark-making or a consistent style to achieve it. Rhythm can be created by repeating shapes, intervals or directional lines.
统一意味着所有部分协调一致；通过有限的调色板、重复的笔触或一致的风格来实现。节奏可以通过重复形状、间隔或方向线来创造。
4. Colour Theory Quick Equations | 色彩理论速查公式
Primary equation: Red + Yellow = Orange; Red + Blue = Violet; Yellow + Blue = Green.
原色公式：红 + 黄 = 橙；红 + 蓝 = 紫；黄 + 蓝 = 绿。
Tertiary colours are made by mixing one primary with one secondary, for example Red + Orange = Red-Orange.
三色由一种原色与一种间色混合，例如红 + 橙 = 红橙。
Tint + Shade + Tone: White + hue = tint; Black + hue = shade; Grey + hue = tone.
加白为浅色调，加黑为深色调，加灰为灰色调。
Relationship formulas: complementary = opposites on the colour wheel; analogous = neighbours; triadic = three equally spaced hues; split-complementary = one hue + two neighbours of its opposite.
色彩关系公式：互补色 = 色轮相对；近似色 = 相邻；三色组合 = 等距三色；分裂补色 = 一色 + 其补色两侧的两色。
Colour temperature rule: warm colours advance, cool colours recede. Use this to create depth without changing drawing accuracy.
色彩温度规则：暖色前进，冷色后退。利用这一规则可在不改变造型准确度的情况下创造空间深度。
5. Composition and Golden Ratio | 构图与黄金比例
Rule of thirds: divide the frame into 3 × 3; place the focal point at one of the four intersections. This is the fastest compositional formula for coursework and exam pieces.
三分法：将画面分为 3 × 3，把焦点放在四个交点之一。这是课程作业和考试作品最快的构图公式。
Golden ratio φ ≈ 1.618: φ = (1 + √5) ÷ 2. Use it to place the horizon, crop the main mass, or divide positive and negative space.
黄金比例 φ ≈ 1.618：φ = (1 + √5) ÷ 2。用它来安排地平线、裁切主体或分割正负空间。
Leading lines formula: dominate diagonal + secondary curve + closure point = directed eye movement. The eye follows the strongest line first.
引导线公式：主导斜线 + 次要曲线 + 终点闭合 = 定向视线运动。眼睛首先跟随最强线条。
Visual balance formula: visual weight ≈ size × contrast × colour intensity × distance from centre. Larger, darker, more saturated and off-centre shapes weigh more.
视觉平衡公式：视觉重量 ≈ 大小 × 对比度 × 色彩强度 × 离中心距离。较大、较暗、较饱和、偏离中心的形状更重。
6. Perspective and Depth Formulas | 透视与空间深度公式
One-point perspective: 1 vanishing point + 1 horizon line + parallel front plane = depth.
一点透视：1 个消失点 + 1 条地平线 + 平行正面 = 深度。
Two-point perspective: 2 vanishing points on the horizon + vertical edges = corner view. Keep both vanishing points off the page for natural proportions.
两点透视：地平线上 2 个消失点 + 垂直边缘 = 转角视角。把两个消失点放在画面外可获得自然比例。
Atmospheric perspective: distance × (haze + reduced contrast + cooler colour + less detail) = depth. Distant objects appear lighter, bluer and softer.
空气透视：距离 ×（雾气 + 对比降低 + 冷色 + 细节减少）= 深度。远处物体显得更亮、更蓝、更柔和。
Size-distance rule: apparent size ∝ 1 ÷ distance. An object twice as far appears roughly half the height when measured by sighting.
大小-距离规则：视在大小 ∝ 1 ÷ 距离。通过目测比较，距离两倍的物体视高约一半。
7. Tonal Value and Shading Rules | 明暗调子与排线定理
Form = highlight + light tone + mid-tone + core shadow + reflected light + cast shadow.
立体感 = 高光 + 亮部 + 中间调 + 明暗交界线 + 反光 + 投影。
Use a 9-step value scale from 0 (white) to 9 (black). A normal pencil drawing should include at least five distinct steps to avoid a flat image.
使用从 0（白）到 9（黑）的九级明度表。普通铅笔画应至少包含五个清晰明度层次，以避免画面平淡。
Shading technique formulas: parallel hatching = direction + spacing; cross-hatching = two overlapping hatches; stippling = dot density; scumbling = small scribbled layers.
排线公式：平行排线 = 方向 + 间距；交叉排线 = 两组重叠排线；点画 = 点的密度；乱线涂擦 = 小笔触层层叠加。
Cast shadow rule: cast shadow falls away from the light source; its edge softens as distance from the object increases.
投影规则：投影远离光源落下；离物体越远，边缘越柔和。
8. Human Proportion and Portrait Rules | 人体与肖像比例规则
Average adult figure ≈ 7.5 to 8 heads tall. Key landmarks: hip at about 4 heads, wrists at about 5 heads, knees at about 6 heads.
成人体型约 7.5 至 8 个头高。关键点：髋部约在 4 个头高处，手腕约 5 个头高，膝盖约 6 个头高。
Face formula: eyes sit at the vertical midpoint of the head; the nose base is halfway from eyes to chin; the mouth is about one-third from nose to chin.
面部比例公式：眼睛在头部垂直中点；鼻底在眼睛到下巴的一半；嘴巴约在鼻底到下巴的三分之一处。
Portrait width rule: face width ≈ five eye-widths; eye spacing = one eye-width; ear length ≈ nose length.
肖像宽度规则：面部宽度约等于五只眼睛的宽度；双眼间距约一只眼宽；耳朵长度约等于鼻子长度。
Hands and feet: hand length ≈ face height from chin to hairline; foot length ≈ one head height.
手和脚：手长约等于下巴到发际线的脸高；脚长约等于一个头高。
9. Annotation and Artist Analysis Formula | 注释与艺术家分析公式
Use the formula Describe + Analyse + Interpret + Judge (DAIJ) for annotation and artist research.
注释与艺术家分析使用公式：描述 + 分析 + 阐释 + 判断（DAIJ）。
Describe: What materials, techniques, colours, shapes, scale and subject? Analyse: How are elements and principles used? Interpret: Why did the artist choose this? Judge: How successful is it and what does it inspire in your own work?
描述：什么媒介、技术、色彩、形状、尺度和主题？分析：如何运用元素与原则？阐释：艺术家为什么这样选择？判断：效果如何，以及它给你的创作带来什么启发？
Personal response sentence formula: ‘In my work, I used [element/principle] inspired by [artist], because [reason], and the outcome was [effect].’ This creates AO3 links.
个人回应句式：’在我的作品中，我借鉴了 [艺术家] 的 [元素/原则]，因为 [原因]，结果是 [效果]。’ 这样可建立 AO3 关联。
Avoid empty praise; use specific visual evidence: ‘The low viewpoint and strong diagonal make the figure appear monumental.’
避免空泛赞美；使用具体的视觉证据：’低视角和强烈斜线使人物显得庄重。’
10. Exam-Day Process Formula | 考试日流程公式
Final piece formula: research (AO1) → experiments (AO2) → development studies (AO3) → personal final outcome (AO4).
最终作品公式：研究（AO1）→ 实验（AO2）→ 发展性研究（AO3）→ 个性化最终成果（AO4）。
In the timed exam, spend about 10% of time planning, 70% making, 10% reviewing, 10% annotating and refining.
在限时考试中，用约 10% 的时间规划、70% 制作、10% 检查、10% 注释与完善。
Self-check formula: every 20 minutes ask — Is my focal point clear? Are tones full-range? Is the composition balanced? Is my annotation linking to artists and AO3?
自检公式：每 20 分钟问自己——焦点清晰吗？明暗层次完整吗？构图平衡吗？注释是否联系艺术家并指向 AO3？
Before stopping, photograph or scan your work
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