📚 IGCSE Edexcel Art: Quick Reference Handbook of Formulas and Principles | IGCSE Edexcel 艺术：公式定理速查手册
Art may not come with chemical equations or algebraic formulas, but it is built upon a rich system of principles, ratios, and colour relationships that function much like formulas. This handbook consolidates the essential ‘formulas’ every IGCSE Edexcel Art student needs, from colour theory to compositional mathematics, helping you create visually compelling and technically sound artwork.
艺术也许没有化学方程式或代数公式，但它建立在丰富的原则、比例和色彩关系之上，这些运作起来非常像公式。本手册汇集了每位 IGCSE Edexcel 艺术学生必备的核心“公式”，从色彩理论到构图数学，帮助你创作出视觉上引人入胜且技法扎实的艺术作品。
1. The Colour Wheel and Colour Theory | 色轮与色彩理论
The colour wheel is the fundamental tool for understanding colour relationships. Sir Isaac Newton developed the first circular diagram of colours in 1666, and the modern 12-part wheel is built from three primary colours: red, yellow, and blue. These cannot be created by mixing other hues.
色轮是理解色彩关系的基本工具。艾萨克·牛顿爵士在 1666 年发明了第一个圆形色彩图表，而现代十二色色轮是基于三种原色构建的：红、黄、蓝。这些颜色无法通过混合其他色调得到。
Secondary colours — orange, green, and violet — are formed by mixing two primaries in equal amounts. Tertiary colours then fill the gaps between primary and secondary hues: red-orange, yellow-orange, yellow-green, blue-green, blue-violet, and red-violet. This gives a continuous spectrum of 12 pure hues.
二次色——橙色、绿色和紫色——是通过等量混合两种原色得到的。三次色则填补原色与二次色之间的空隙：红橙、黄橙、黄绿、蓝绿、蓝紫和红紫。这就形成了一个连续的 12 种纯色相环。
| Colour Category | Mixing Formula | Example Hues |
|---|---|---|
| Primary | Cannot be mixed | Red, Yellow, Blue |
| Secondary | Primary + Primary | Orange (R+Y), Green (Y+B), Violet (B+R) |
| Tertiary | Primary + Secondary | Red-Orange, Yellow-Green, etc. |
Understanding this hierarchy makes colour mixing predictable. For IGCSE coursework, a confident handling of the wheel shows examiners you can control hue with intention rather than by accident.
理解这一层级关系让色彩混合变得可预测。在 IGCSE 课程作业中，能否自信地驾驭色轮向考官展示了你能够有意识地控制色调，而非偶然碰巧。
2. Complementary and Analogous Colours | 互补色与类似色
Complementary colours sit directly opposite each other on the colour wheel. Pairs such as red and green, blue and orange, or yellow and violet create maximum contrast and visual vibration when placed side by side. This is because each complementary pair contains one warm and one cool hue, stimulating different cones in the eye simultaneously.
互补色位于色轮上彼此正对的位置。红与绿、蓝与橙、黄与紫等成对色彩并置时，会产生最强的对比和视觉振动。这是因为每对互补色都包含一个暖色和一个冷色，同时刺激眼睛中不同的视锥细胞。
Mixing two complements in paint yields a neutral gray or brown, depending on proportions. This is an essential formula for toning down a colour without adding black — simply add a tiny amount of its complement. For example, a too-vivid red can be quietened with a touch of green.
在颜料中混合两种互补色会产生中性灰色或棕色，具体取决于比例。这是一个不用加黑就能降调颜色的关键公式——只需加入极少量的其互补色。例如，过于鲜亮的红色可以用一点绿色来降低其鲜艳度。
Analogous colours, in contrast, are neighbours on the wheel, such as blue, blue-green, and green. They create harmonious, serene palettes often found in nature. Using analogous colours with one complementary accent is a reliable formula for a balanced composition.
类似色则相反，它们是色轮上的邻居，例如蓝、蓝绿和绿。它们营造出和谐、宁静的调色板，常见于自然界。使用类似色搭配一个互补色作为点缀，是实现构图平衡的可靠公式。
3. Warm and Cool Colours | 暖色与冷色
The colour wheel can be split in half: warm colours range from red through orange to yellow, while cool colours span green through blue to violet. Warm hues appear to advance in a painting, making objects feel closer; cool hues recede, pushing elements into the background.
色轮可以分成两半：暖色从红经橙到黄，而冷色从绿经蓝到紫。暖色在绘画中看上去向前推移，使物体感觉更近；冷色则后退，把元素推入背景。
Temperature is relative, not absolute. A blue-violet can appear warm when placed next to an icy blue-green, yet cool beside a red-orange. Mastering temperature shifts allows artists to model form without relying on black shadow tones, which can deaden a painting.
色温是相对的，而非绝对的。一个蓝紫色放在冰蓝绿旁边会显得暖，但在红橙旁边则显得冷。掌握色温转换能让艺术家在塑造形体时不必依赖会使画面沉闷的黑色阴影调子。
A quick formula for shadows: mix the local colour with its complement plus a little blue to cool it down. For highlights, add a warm yellow or white. This keeps the shadow transparent and the light luminous.
一个快速的阴影公式：将物体固有色与其互补色混合，再加一点蓝使其变冷。高光则加入暖黄或白色。这能保持阴影通透，光线明亮。
4. Hue, Saturation, and Value | 色相、饱和度与明度
Every colour can be described by three properties: hue (the name of the colour, e.g., red, blue-green), saturation (intensity or purity of the colour), and value (lightness or darkness). Think of these as the three coordinates of the colour space.
每一种颜色都可以用三个属性来描述：色相（颜色的名称，如红、蓝绿）、饱和度（颜色的强度或纯度）以及明度（亮度或暗度）。可以把它们想象成色彩空间的三维坐标。
High saturation means a colour is vivid and unmixed; low saturation (desaturated) leans towards gray. Value ranges from 0 (black) to 10 (white) on the Munsell scale. Changing any one property transforms the colour completely. For example, adding white to pure red raises its value and reduces saturation, producing pink.
高饱和度意味着颜色鲜艳且未混合；低饱和度（去色）则趋向灰色。明度在孟塞尔色立体上从 0（黑）到 10（白）。改变任何一个属性都会彻底转变颜色。例如，在纯红中加入白色会提高明度并降低饱和度，产生粉色。
Formula for matching a colour: first match the hue, then adjust value by adding white or black, and finally tweak saturation with its complement. This systematic approach prevents muddy mixing and is especially valuable when working from observation.
配色公式：先匹配色相，然后通过加白或加黑调整明度，最后用其互补色调校饱和度。这种系统的方法可以防止颜料调脏，在写生时尤其有价值。
5. The Rule of Thirds | 三分法则
The rule of thirds divides the canvas into nine equal rectangles using two equally spaced horizontal lines and two equally spaced vertical lines. Placing key elements along these lines or at their intersections creates a more dynamic and balanced composition than centring the subject.
三分法则用两条等距的水平线和两条等距的垂直线将画布分成九个相等的矩形。将关键元素放置在这些线上或它们的交叉点上，能营造出比将主体居中更富动感和平衡的构图。
For a landscape, position the horizon on the upper or lower third rather than cutting the canvas in half. For a portrait, align the eyes on the upper horizontal line. These alignments tap into the way the human eye naturally scans an image, making the artwork feel effortlessly resolved.
画风景时，把地平线放在上方或下方的三分之一处，而不要将画布一分为二。画肖像时，让眼睛对齐上方的水平线。这些对齐方式契合人眼自然扫描图像的方式，使作品看上去毫不费力地协调。
You can see the rule of thirds grid on most camera viewfinders. In art, lightly sketch the grid before committing to a composition. While not a rigid law, this formula provides a reliable starting point for visual organisation.
你可以在大多数相机取景器中看到三分法网格。在艺术创作中，在确定构图前不妨轻轻画出网格。虽然不是硬性法则，但这个公式为视觉组织提供了一个可靠的起点。
6. Golden Ratio and Golden Spiral | 黄金比例与黄金螺旋
The golden ratio, approximately 1 : 1.618, is a mathematical proportion found in nature, from nautilus shells to sunflower seed arrangements. In art, it has been used for centuries to create compositions of exceptional balance and beauty. The ratio is often denoted by the Greek letter φ (phi).
黄金比例大约为 1 : 1.618，是一种存在于自然界中的数学比例，从鹦鹉螺壳到向日葵种子的排列都能见到。在艺术中，它被用了几个世纪来创造格外平衡与优美的构图。该比例常用希腊字母 φ（phi）表示。
A rectangle with sides in the golden ratio can be subdivided into a square and a smaller golden rectangle, generating a logarithmic spiral. Artists like Leonardo da Vinci and Salvador Dalí consciously employed this ‘divine proportion’ to structure their compositions.
一个边长符合黄金比例的矩形可以细分为一个正方形和一个较小的黄金矩形，由此生成一条对数螺旋。像莱奥纳多·达·芬奇和萨尔瓦多·达利这样的艺术家曾自觉地运用这种“神圣比例”来构建构图。
To apply it practically, use the golden rectangle to position focal points. For instance, place the main subject where the spiral tightens, or align the horizon with a golden section line. The formula for the golden section a : b = b : (a+b) where a > b can be approximated by dividing your canvas width by 1.618 to find the key horizontal placement.
实际运用时，用黄金矩形来定位焦点。例如，将主体放在螺旋收紧处，或者将地平线与黄金分割线对齐。黄金分割公式 a : b = b : (a+b)，其中 a > b，你可以近似地把画布宽度除以 1.618 来找到关键的横向放置点。
7. Linear Perspective: One-Point and Two-Point | 线性透视：一点透视与两点透视
Linear perspective creates the illusion of depth on a flat surface using converging lines. In one-point perspective, all receding parallel lines meet at a single vanishing point on the horizon line. This is ideal for compositions facing directly towards the viewer, like a central corridor or a road disappearing into the distance.
线性透视利用会聚的线条在平面上营造深度幻觉。在一点透视中，所有后退的平行线都汇聚于地平线上的一个消失点。这适合正面朝向观众的构图，如中央走廊或消失在远方的道路。
Two-point perspective uses two vanishing points placed on the horizon, typically outside the picture plane. Vertical lines remain vertical, but orthogonal lines recede to either left or right vanishing point. This system is essential for drawing objects seen at an angle, such as the corner of a building.
两点透视使用地平线上的两个消失点，通常位于画面之外。垂直线保持垂直，但正交线分别向左边或右边的消失点后退。这个系统对于表现从某个角度看到的物体至关重要，例如建筑的转角。
Perspective formula: all parallel lines in a given set share the same vanishing point. Objects become smaller as they approach the vanishing point, following the law of proportional diminution. The height of the horizon line corresponds to the viewer’s eye level, anchoring the entire scene.
透视公式：同一组平行线共享同一个消失点。物体在靠近消失点时变小，遵循比例缩减法则。地平线的高度对应观者的视平线，是整个场景的锚点。
8. Atmospheric Perspective | 大气透视
Atmospheric perspective, also called aerial perspective, simulates the effect of air and light over distance. Distant objects appear lighter in value, lower in contrast, cooler in colour temperature, and less detailed than those in the foreground. Leonardo da Vinci described this as ‘the perspective of disappearance’.
大气透视，也称空气透视，模仿空气和光在远距离上的影响。远处的物体比前景中的物体明度更高、对比度更低、色温偏冷且细节更少。莱奥纳多·达·芬奇将其描述为“消失透视”。
Formula: as distance increases, add sky colour to the local colour of objects — typically a pale blue or violet. Reduce saturation and blur edges slightly. This technique is especially powerful in landscape painting, where mountain ranges can be rendered almost as flat silhouettes with a bluish tint.
公式：随着距离增加，向物体的固有色中加入天空色——通常是淡蓝或淡紫。降低饱和度，并稍微模糊边缘。这种技法在风景画中格外有力，山脉可以几乎被表现为带蓝色调的扁平剪影。
The shift in value can be pre-mixed: mix the foreground colour, then add white plus a touch of ultramarine blue to create the same hue for a middle-distance plane. Add more white and blue for the far distance. This value gradation reinforces depth even without linear perspective.
明度的变化可以预先调好：调出前景色，然后加入白色加上少许群青，为中间距离的景层面创造出相同色相。更远距离则加入更多白色和蓝色。这种明度渐变即使没有线性透视也能增强深度感。
9. Shading and Value Scales | 明暗与明度等级
Shading uses value to describe form. The classic shading model involves five elements: highlight, halftone, core shadow, reflected light, and cast shadow. Each element corresponds to how light falls on and around an object. A sphere under a single light source is the standard exercise to master this system.
明暗运用明度来表现形体。经典明暗模型包含五个要素：高光、中间调、明暗交界线、反光和投影。每个要素对应着光线如何落在物体上和其周围。单一光源下的球体是掌握该体系的标准练习。
A value scale usually has 9 or 10 steps from pure white to pure black. Practising a smooth gradient trains hand control for achieving even tone. In pencil drawing, the formula for a mid-tone is hatching at 45°; cross-hatching at 90° builds darker values. The pressure and spacing of marks govern the perceived darkness.
明度等级通常从纯白到纯黑有 9 到 10 个阶梯。练习平滑渐变可以训练手部控制，以获得均匀的色调。在铅笔画中，中间调的公式是 45° 排线；90° 交叉排线可构建更暗的明度。笔触的压力和间距决定感知的暗度。
Cast shadows follow light logic: the edge closest to the object is sharper, becoming softer further away. Reflected light inside the shadow is never as bright as the lit side. Remember the formula: core shadow is darker than the cast shadow, which is darker than the reflected light.
投影遵循光线逻辑：离物体最近的边缘较锐利，越远越模糊。阴影内部的反光永远不如亮面亮。记住这个公式：明暗交界线比投影暗，投影比反光暗。
10. Proportion and the Human Figure | 比例与人体
Proportion governs the relative sizes of parts within a whole. In figure drawing, the classical ideal is eight heads tall: the body from top to pubic bone measures four heads, the legs another four. The eyes sit at the halfway mark of the head, and the navel aligns with three heads down from the top.
比例支配着整体中各部分相对的大小。在人物素描中，古典理想身高是八个头长：从头顶到耻骨为四个头，双腿再占四个头。眼睛位于头顶到下巴的中点上，肚脐则对应从头顶向下三个头的位置。
These measurements are not rigid rules but useful starting formulas. Actual human proportions vary, but the eight-head canon provides a baseline for constructing believable figures. The width across the shoulders is roughly two head lengths, and the hand spans from chin to hairline.
这些测量并非硬性规则，但可作为有用的起始公式。实际人体比例各有不同，但八头身规范为构建可信的人物形象提供了基线。肩宽约为两头长，手的长度则从下巴到发际线。
For the face, the ‘five-eye rule’ helps: the head is five eye-widths across, with one eye-width between the eyes. The bottom of the nose is halfway between eyes and chin, and the mouth sits one-third down from nose to chin. Repeat these formulas enough, and they become second nature.
对于面部，“五眼法则”很有帮助：头部宽度相当于五只眼睛，双眼之间相距一只眼睛。鼻底位于眼睛和下巴的中点上，嘴巴位于鼻子到下巴的下三分之一处。反复运用这些公式，它们就会变得像第二天性一样。
11. Compositional Balance and Unity | 构图的平衡与统一
Balance in composition refers to the distribution of visual weight. Symmetrical balance (formal) places identical elements on either side of a central axis, conveying stability and formality. Asymmetrical balance (informal) uses dissimilar elements that feel equally weighted, often through contrast of colour, size, or texture.
构图的平衡指的是视觉重量的分布。对称平衡（形式平衡）将相同的元素放置在中心轴的两侧，传达出稳定与庄重。非对称平衡（非形式平衡）则使用不同但感觉重量相等的元素，通常通过色彩、大小或质感的对比来实现。
A dark small shape can balance a large light area; a textured patch balances a smooth expanse. The formula for achieving asymmetrical balance: visual weight = size × contrast × position. An element near the edge feels heavier than the same element near the centre.
一个深色的小形状可以平衡一大片浅色区域；一块有肌理的面可平衡一片光滑的面。实现非对称平衡的公式：视觉重量 = 大小 × 对比度 × 位置。靠近边缘的元素比同样元素靠近中心感觉更重。
Unity is the sense that all parts belong together. Repetition of a colour, shape, or line quality creates cohesion. The rule of odds — grouping elements in threes or fives rather than even numbers — often enhances unity because the eye cannot pair them symmetrically and instead moves through the composition.
统一感是指所有部分都归属于整体的感觉。重复某种颜色、形状或线条品质能创造出凝聚力。奇数法则——将元素按三个或五个而非偶数分组——常常能增强统一感，因为眼睛无法将其对称配对，从而在构图中流动。
12. The Fibonacci Sequence in Art | 艺术中的斐波那契数列
The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21…) appears repeatedly in natural growth patterns, and artists have used it to create organic, pleasing rhythms. The ratio of consecutive Fibonacci numbers approximates the golden ratio: 5/3 = 1.666, 8/5 = 1.6, 13/8 = 1.625, converging to 1.618.
斐波那契数列（0, 1, 1, 2, 3, 5, 8, 13, 21……）反复出现在自然生长模式中，艺术家用它来创造有机、令人愉悦的节奏。相邻斐波那契数的比值接近黄金比例：5/3 = 1.666，8/5 = 1.6，13/8 = 1.625，并逐渐逼近 1.618。
A Fibonacci spiral can be constructed by drawing quarter-circles inside squares whose side lengths follow the sequence. This spiral guides the viewer’s eye along a natural flow path. Placing the area of greatest interest at the spiral’s culmination — the ‘eye’ — creates a strong focal point.
斐波那契螺旋可以通过在一系列边长为数列值的正方形内画四分之一圆来构建。这条螺旋引导观者的视线沿着一种自然的流动路径移动。将最感兴趣的区域放置在螺旋的汇聚处——“眼睛”——就能营造出强烈的焦点。
In practical terms, you can use Fibonacci numbers to determine proportions: a 5 x 8-inch canvas, or a layout where the main figure occupies 3 sections of a 5-section grid. The sequence offers a flexible, nature-based alternative to the static rule of thirds, injecting dynamic growth into composition.
实际操作中，你可以用斐波那契数来确定比例：一块 5 × 8 英寸的画布，或者把主要人物安排在一个五等分网格中占据三份。这一数列为静态的三分法则提供了一种灵活、基于自然的替代方案，为构图注入动态的生长感。
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