📚 GCSE CAIE Art: Quick Reference of Formulas & Principles | GCSE CAIE 艺术：公式定理速查手册
Art may seem to be all about free expression, but behind every successful composition lie repeatable 'formulas' and principles that guide the eye, balance the frame, and evoke emotion. This quick reference brings together the essential colour equations, perspective rules, proportion ratios, and design laws that every GCSE CAIE Art student should have at their fingertips. Use these as your creative toolkit for both personal portfolio work and the externally set assignment.
艺术看似全凭自由表达，但每一件成功的作品背后，都有可重复使用的'公式'和原理在引导视线、平衡画面并激发情感。这本速查手册汇集了每一位 GCSE CAIE 艺术学生都应熟记的基本色彩方程式、透视法则、比例黄金数和设计定律。将其作为你的创意工具箱，用于个人作品集和外部统考作业。
1. Colour Mixing Formulas | 色彩混合公式
Colour mixing follows predictable mathematical relationships. Understanding these gives you control over your palette and prevents muddy colours.
色彩混合遵循可预测的数学关系。理解它们，你就能掌控调色板，避免出现脏色。
Subtractive mixing (paint/ink): een; Magenta + Yellow = Red; Cyan + Magenta + Yellow = Black (or muddy brown in practice).
减色混合（颜料/油墨）：青 + 品红 = 蓝；青 + 黄 = 绿；品红 + 黄 = 红；青 + 品红 + 黄 = 黑（实践中呈脏棕色）。
Additive mixing (light): d + Green = Yellow; Red + Blue = Magenta; Green + Blue = Cyan; Red + Green + Blue = White.
加色混合（光）：红 + 绿 = 黄；红 + 蓝 = 品红；绿 + 蓝 = 青；红 + 绿 + 蓝 = 白。
Complementary neutralisation: Orange = Grey; Yellow + Purple = Grey. Use this to tone down colours without adding black.
互补色中和：红 + 绿 = 灰；蓝 + 橙 = 灰；黄 + 紫 = 灰。用这个技巧来降低色彩纯度，无需加入黑色。
2. Colour Harmony Formulas | 色彩和谐公式
Harmonious colour schemes are based on simple geometric relationships on the colour wheel. Here are the key formulas to produce balance and contrast deliberately.
和谐的色彩方案基于色轮上简单的几何关系。以下是刻意创造平衡感和对比感的关键公式。
Analogous (adjacent colours): Choose any 3-5 neighbouring hues, e.g. blue, blue-green, green. Always harmonious, low contrast.
类似色（相邻色）：选取任意 3-5 个相邻色相，如蓝、蓝绿、绿。始终和谐，对比度低。
Complementary (opposite pairs): Pick 2 hues directly opposite, e.g. red & green, blue & orange. Maximum contrast and vibrancy.
互补色（对立色对）：选取 2 个正对的色相，如红与绿、蓝与橙。对比最大，画面响亮。
Split-complementary: One base colour plus the two colours adjacent to its complement, e.g. blue with yellow-orange and red-orange. High contrast but softer than straight complementary.
分裂互补色：一个基色加其互补色两侧的两个颜色，例如蓝配黄橙和红橙。对比强烈但比直接互补更柔和。
Triadic: Three colours evenly spaced (120° apart), e.g. red, yellow, blue. Vibrant, balanced when one dominates and others are accents.
三色组：三个等距分布的颜色（相隔 120°），如红、黄、蓝。响亮，当一种颜色主导、其余用作强调时效果平衡。
3. Perspective Rules & Formulas | 透视法则与公式
Linear perspective creates the illusion of depth on a flat surface using vanishing points and converging lines. Master these formulas to construct believable space.
线透视利用消失点和会聚线在平面上创造纵深感。掌握这些公式，构建令人信服的空间。
One‑point perspective: All receding lines converge to one central vanishing point on the horizon line. Use for roads, railways, corridors.
一点透视：所有向后延伸的线条汇聚到视平线上的一个中心消失点。用于道路、铁路、走廊。
Two‑point perspective: Vertical edges remain parallel; horizontal edges recede to two separate vanishing points on the horizon. Best for drawing corners of buildings.
两点透视：垂直棱边保持平行；水平棱边向两个不同的消失点汇聚在视平线上。最合适用于画建筑转角。
Foreshortening formula: The apparent size of an object is inversely proportional to its distance from the viewer. If distance doubles, size halves.
前缩法公式：物体表现大小与离观者的距离成反比。距离翻倍，尺寸减半。
Aerial perspective (atmospheric): Distant objects appear lighter, less detailed, and bluer/cooler due to atmospheric haze. Value contrast decreases with distance.
空气透视（大气透视）：远处物体因大气雾霭显得更浅、细节更少、更偏蓝/冷。明度对比随距离增加而减弱。
4. Composition Formulas | 构图公式
Composition determines how the viewer's eye travels through the artwork. These time-tested formulas help establish focal points and visual flow.
构图决定了观众的视线如何穿过作品。这些久经考验的公式有助于确立焦点和视觉流动。
Rule of thirds: ×3 grid. Place key elements along the lines or at intersections to create dynamic balance.
三分法：将画面分成 3×3 网格。把关键元素放在这些线条或交点上，营造动态平衡。
Golden ratio (φ ≈ 1.618): The golden section creates a division where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. Use a golden rectangle or spiral to place focal points.
黄金比例（φ ≈ 1.618）：黄金分割使整体与较大部分的比率等于较大部分与较小部分的比率。使用黄金矩形或螺旋线放置焦点。
Leading lines formula: Position lines (roads, branches, rivers) so they converge toward the main subject, literally leading the eye. Diagonal lines imply movement.
导向线公式：布置线条（道路、树枝、河流）使其汇聚到主主体，真正引导视线。对角线暗示动感。
Symmetry & asymmetry: nce). Asymmetry = careful arrangement of unequal visual weights creating informal balance.
对称与不对称：对称 = 完美镜像（正式平衡）。不对称 = 不同视觉重量的精心安排，创造非正式平衡。
5. Human Figure Proportion Formulas | 人体比例公式
Accurate figure drawing relies on standardised proportions. These canonical formulas serve as a starting point, which you can then adapt for individual differences.
准确的人体绘制依赖标准化比例。这些规范公式可作为起点，之后可按个体差异调整。
Canon of 8 heads: An ideal adult figure is about 8 head-lengths tall. Key landmarks: chin to nipples (2 heads down), to navel (3 heads), to pubis (4 heads), mid-thigh (5 heads), knees (6 heads), mid-shin (7 heads).
八头身法则：理想成人身高约相当于 8 个头长。关键定位：下巴至乳头（2 头长），至肚脐（3 头），至耻骨（4 头），大腿中部（5 头），膝盖（6 头），小腿中部（7 头）。
Face proportions: Eyes sit halfway down the head. The face from hairline to chin can be divided into equal thirds: forehead, nose, mouth/chin. The space between eyes equals the width of one eye.
面部比例：眼睛位于头部垂直中点。从发际线到下巴可等分为三庭：上额头、中鼻子、下嘴巴/下巴。两眼间距等于一只眼的宽度。
Arm span ≈ height: The distance from fingertip to fingertip with arms outstretched is roughly equal to the person's full height.
臂展 ≈ 身高：双臂平伸时指尖到指尖的距离大致等于全身身高。
6. Tone and Value Contrast Formulas | 色调与明度对比公式
Value – the lightness or darkness of a colour – is the backbone of form. These formulas help you create volume, drama, and depth through controlled contrast.
明度——颜色的深浅——是塑造形体的支柱。这些公式帮你通过控制对比来创造体积感、戏剧性和纵深感。
9‑step value scale: From pure white (1) to pure black (9). A full‑range drawing uses at least 5–7 distinct steps. Squint to simplify values into light, medium, and dark masses.
9 级明度尺：从纯白（1）到纯黑（9）。一幅全调子素描至少要用 5–7 个不同的明度级。眯眼观察可将明度简化成亮、灰、暗三个大块面。
Chiaroscuro formula: he opposite side + core shadow (the darkest part of the form shadow) + reflected light + cast shadow. The greatest contrast is placed near the light source.
明暗对照法公式：强光源 → 背面深阴影 + 明暗交界线（形体暗面中最暗部）+ 反光 + 投影。最大对比靠近光源放置。
Low‑key vs high‑key: Low‑key = predominantly dark values, dramatic. High‑key = predominantly light values, airy. Mid‑key = mostly mid‑tones. Choose based on mood.
低调 vs 高调：低调 = 以暗明度为主，戏剧性强。高调 = 以浅明度为主，轻盈通透。中调 = 以中间明度为主。根据氛围选择。
7. Colour Temperature & Psychology Formulas | 色温与心理效应公式
Colour temperature influences spatial perception and emotional response. Use these formulas to guide the mood and depth of your artwork.
色温影响空间感和情感反应。用这些公式来引导作品的氛围与深度。
Temperature rule of depth: Warm colours (reds, oranges, yellows) advance toward the viewer; cool colours (blues, greens, purples) recede. Place warm hues in foreground, cool in background for maximum depth.
色温深度法则：暖色（红、橙、黄）向观者前进；冷色（蓝、绿、紫）后退。将暖色放在前景，冷色放在背景以获得最大纵深感。
Warm + cool contrast formula: Placing a warm colour next to a cool colour intensifies both. For example, an orange sun looks hotter against a blue sky.
冷暖对比公式：将暖色与冷色并列放置会增强彼此。例如，橙色太阳在蓝色天空映衬下显得更加炽热。
Psychological associations: vy; Purple = royalty, mystery; Black = power, elegance, death; White = purity, simplicity.
心理联想：红 = 激情、危险、能量；蓝 = 平静、信任、悲伤；黄 = 快乐、警示；绿 = 自然、成长、嫉妒；紫 = 皇家、神秘；黑 = 权力、优雅、死亡；白 = 纯洁、简约。
8. Texture & Pattern Formulas | 肌理与图形公式
Texture and pattern bring surface quality and rhythm to a composition. These repeatable formulas help you invent, stylise, and unify surfaces.
肌理与图形为构面带来表面质感与节奏感。这些可重复的公式帮助你创造、风格化和统一表面。
Mark‑making for texture: Hatching (parallel lines), cross‑ rokes). Dense marks = dark value/smooth implied texture; spaced marks = light value/rough.
纹理笔触：排线（平行线）、交叉排线（成角度层叠线条）、点画（点）、乱线（松散环形笔触）。密集笔触 = 暗明度/暗示光滑肌理；分散笔触 = 浅明度/粗糙感。
Pattern repeat formulas: Full drop (grid repetition), half drop (staggered like brickwork), mirror and rotational symmetry. Use patterns to create visual rhythm and unity.
图案重复公式：完全平铺（网格重复）、半平铺（像砖墙般错位排列）、镜像和旋转对称。用图案创造视觉节奏与统一感。
Texture contrast: Juxtapose a rough, impasto area with a smooth, glazed area. The eye will be drawn to the textured zone� use this to emphasise your focal point.
肌理对比：将粗糙厚涂的区域与光滑、罩染的区域并置。视线会被吸引到肌理区域——利用这一点来强调你的焦点。
9. Spatial Depth Formulas (Beyond Perspective) | 空间深度公式（透视之外）
Even without linear perspective, you can create a convincing illusion of depth using overlapping, scale, position, and edge control. These are the painter's spatial shortcuts.
即使没有线透视，你也可以利用重叠、比例、位置和边缘处理来创造逼真的纵深感。这些是画家营造空间的捷径。
Overlap rule: Objects that cover part of another are perceived as closer. Always place foreground elements overlapping middle‑ and background forms.
重叠法则：遮挡另一个物体一部分的对象被感知为更近。始终将前景元素重叠在中景和背景形之上。
Size and placement: Larger shapes appear nearer; smaller shapes appear farther. Objects placed lower in the picture plane tend to read as closer (ground plane assumption).
尺寸与放置位置：较大的形状看起来更近；较小的形状显得更远。放置在画面较低处的物体往往被理解为更近（基于地平面假设）。
Edge quality formula: Sharp, crisp edges advance; soft, blurred edges recede. Combine with atmospheric perspective: distant edges are softer and lower in contrast.
边缘质感公式：锐利清晰的边缘向前推进；柔和模糊的边缘向后退。结合空气透视：远处边缘更柔和且对比度更低。
10. Principles of Design | 设计原则公式
The design principles are the fundamental laws for organising visual elements. Think of them as the 'grammar' of art that ensures your composition communicates effectively.
设计原则是组织视觉元素的基本法则。可将其视为艺术的'语法'，确保你的构图有效地传递信息。
Balance: ; asymmetrical = unequal but visually equal weight; radial = balance from a central point.
平衡：视觉重量的分布。对称 = 镜式；不对称 = 不相等但视觉重量相当；放射 = 以中心点为依据的平衡。
Emphasis (dominance): The artist makes one area stand out by manipulating contrast, placement, isolation, or scale. Everything else supports this focal point.
强调（主导）：艺术家通过操控对比、位置、孤立或比例使某一区域突出。其他一切都为这个焦点服务。
Unity with variety: terest (contrasting shapes, textures). The formula: enough repetition to unify, enough contrast to avoid monotony.
统一与变化：统一 = 所有部分属于一个整体（重复、邻近、色彩和谐）。变化 = 增加趣味的差异（对比形状、质感）。公式：足够的重复来统一，足够的对比来避免单调。
Movement/rhythm: Repetition of elements (lines, shapes, colours) creates a visual beat. Curves, diagonals, and spirals imply movement. Staggered spacing speeds up rhythm; even spacing slows it down.
运动/节奏：元素的重复（线条、形状、颜色）创造视觉节拍。曲线、对角线和螺旋线暗示运动。错位间距加快节奏；均匀间距放慢它。
11. Photography Exposure Triangle | 摄影曝光三角公式
For students working in lens‑based and light‑based media, the exposure triangle is an essential technical formula that governs image brightness and creative effects.
对于使用镜头和光媒介的学生来说，曝光三角是控制图像亮度和创意效果的重要技术公式。
Aperture (f‑stop) × Shutter Speed × ISO = Exposure Value. Changing one requires adjusting another to maintain the same exposure. Like balancing an equation.
光圈（f 值）× 快门速度 × 感光度 = 曝光值。改变一个参数就需要调整另一个以保持相同曝光。就像平衡方程一样。
Wider aperture (e.g. f/2.8) → more light, shallow depth of field (blurred background). Narrower aperture (f/16) → less light, deep focus.
大光圈（如 f/2.8）→ 更多进光，浅景深（背景虚化）。 小光圈（f/16）→ 较少进光，深景深。
Fast shutter (1/1000s) → freezes motion. Slow shutter (1/30s or longer) → motion blur. Increase ISO to compensate in low light, but higher ISO → more noise/grain.
高速快门（1/1000 秒）→ 凝固运动。慢速快门（1/30 秒或更长）→ 运动模糊。在弱光下提高 ISO 作为补偿，但高 ISO → 更多噪点/颗粒。
12. Typography Pairing Formula | 字体搭配公式
For graphic communication projects, choosing typefaces is not random. These pairing formulas guarantee legibility and visual hierarchy.
在平面传达项目中，选择字体并非随性而为。这些搭配公式确保可读性和视觉层次。
Serif + Sans‑serif contrast: Pair a classic serif (e.g. Garamond, Times) for headings with a clean sans‑serif (e.g. Helvetica, Arial) for body copy, or vice versa. This creates instant typographic tension and clarity.
衬线 + 无衬线对比：将经典衬线体（如 Garamond、Times）用于标题，搭配干净的无衬线体（如 Helvetica、Arial）用于正文，或反之。这立即创造出字体间的张力与清晰感。
Limit to 2–3 typefaces: One for main headings, one for subheadings, one for body text. Too many fonts disrupt unity. Use weight (bold, regular, light) and style (italic) to create variation within one typeface family.
限定 2–3 种字体：一种做主标题，一种做副标题，一种做正文。太多字体破坏统一感。使用字重（粗、常规、细）和样式（斜体）在同一个字体家族内创造变化。
Hierarchy formula: t, most readable. Consistent spacing between these levels builds a clear visual structure.
层次公式：最重要信息 = 最大、最粗、最高对比度。第二层 = 略小。正文 = 最小、最易读。这些层级之间一致的间距建立起清晰的视觉结构。
Published by TutorHao | Art Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图