Art Formula & Theorem Quick Reference Handbook | 艺术公式定理速查手册

📚 Art Formula & Theorem Quick Reference Handbook | 艺术公式定理速查手册

This handbook compiles the essential formulas, theorems and principles used in KS3 AQA Art & Design. Understand colour mixing, composition, perspective and proportion with quick reference notes, each illustrated with clear bilingual explanations.

本手册汇编了 KS3 AQA 艺术与设计中使用的基本公式、定理和原理。通过清晰的双语说明和速查笔记，帮助你快速掌握色彩混合、构图、透视和比例等核心知识。

1. The Colour Wheel Foundation | 色轮基础

The traditional RYB colour wheel arranges hues in a circle. Primary colours (red, yellow, blue) are spaced 120° apart, forming an equilateral triangle. Secondary colours sit exactly midway between their parent primaries, creating a balanced 6‑step wheel. The angular distance between any two hues determines their relationship: adjacent colours (30° apart) are analogous, opposite colours (180° apart) are complementary.

传统的红黄蓝色轮将色相排列成圆。三原色（红、黄、蓝）以 120° 间距分布，构成等边三角形。二次色恰好位于其母原色的正中间，形成均衡的六步色轮。任意两种色相的夹角决定其关系：相邻色（相距 30°）为类似色，对角色（相距 180°）为互补色。

Colour wheel formula: R (0°) → Y (120°) → B (240°) → back to R. The secondary hues are derived by averaging the angles: Orange at 60°, Green at 180°, Violet at 300°.

色轮公式：红 (0°) → 黄 (120°) → 蓝 (240°) → 回到红。二次色相通过角度均分得出：橙色在 60°，绿色在 180°，紫色在 300°。

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2. Subtractive Colour Mixing Equations | 减色混合方程

When mixing pigments, light is subtracted from the reflected spectrum. The basic subtractive mixing equations for the RYB primaries are:

颜料混合时，光线从反射光谱中被减去。以红黄蓝为原色的减色混合基本方程如下：

Red + Yellow → Orange

Yellow + Blue → Green

Blue + Red → Violet

红 + 黄 → 橙；黄 + 蓝 → 绿；蓝 + 红 → 紫。

Tertiary colours result from mixing a primary with its neighbouring secondary, giving six additional hues: Red‑Orange, Yellow‑Orange, Yellow‑Green, Blue‑Green, Blue‑Violet, Red‑Violet. The naming convention places the primary first.

三次色由原色与相邻的二次色混合而成，共增加六种色相：红橙、黄橙、黄绿、蓝绿、蓝紫、红紫。命名规则为原色在前。

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3. Complementary and Harmonious Schemes | 互补与和谐配色方案

Complementary colours sit opposite each other on the colour wheel. The complementary pairs in RYB are:

互补色在色轮上彼此相对。红黄蓝色轮的互补对为：

Red ↔ Green    Yellow ↔ Purple    Blue ↔ Orange

红 ↔ 绿    黄 ↔ 紫    蓝 ↔ 橙

Analogous harmonies use 2–4 hues next to each other on the wheel (e.g. blue, blue‑green, green). A triadic scheme connects three colours equally spaced at 120° (e.g. red, yellow, blue). A split‑complementary scheme takes one colour plus the two colours adjacent to its complement, creating strong contrast with less tension.

类似色和谐使用色轮上相邻的 2–4 种色相（如蓝、蓝绿、绿）。三角配色以 120° 等距连接三种颜色（如红、黄、蓝）。分裂互补配色选取一种颜色，再取其互补色两侧的两种颜色，形成强烈对比但冲突较小。

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4. Tints, Shades and Tones | 色调、阴影与调性

The value of a hue is altered by adding white, black or grey. These modifiers follow simple formulas:

色相的值通过加入白、黑或灰来改变。这些调整遵循简单公式：

Tint = Pure Hue + White

Shade = Pure Hue + Black

Tone = Pure Hue + Grey

色调 = 纯色 + 白；阴影 = 纯色 + 黑；调性 = 纯色 + 灰。

Adding white raises the value and reduces saturation, producing a lighter, softer version of the colour. Adding black lowers the value, creating a darker, richer hue. Adding grey mutes the intensity without drastically changing the value, making the colour more natural. In many artworks, a full range of tints, shades and tones creates the illusion of three‑dimensional form.

加白提高明度并降低饱和度，产生更浅、更柔和的变体。加黑降低明度，形成更暗、更浓郁的色相。加灰在不大幅改变明度的情况下抑制纯度，使颜色更自然。在许多艺术作品中，完整的色调、阴影与调性范围可以塑造三维形体感。

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5. One‑Point and Two‑Point Perspective | 一点透视与两点透视

Perspective creates the illusion of depth on a flat surface. The fundamental rule: all parallel lines receding into the distance appear to converge at a vanishing point (VP) on the horizon line (HL).

透视在平面上营造深度错觉。基本规则：所有向远处后退的平行线似乎在视平线上汇聚于一个灭点。

One‑point perspective: Objects face the viewer directly. Height lines remain vertical; width lines remain horizontal. Depth lines converge to a single central VP.

一点透视：物体正面朝向观者。高度线保持垂直，宽度线保持水平，深度线汇聚于中央的单个灭点。

Two‑point perspective: Objects are rotated so corners face the viewer. Vertical edges remain vertical. Two sets of horizontal edges recede to two different VPs placed on the horizon line, typically outside the picture plane.

两点透视：物体旋转使棱角朝向观者。垂直边缘保持垂直，两组水平边缘分别向视平线上的两个不同灭点后退，灭点通常位于画面之外。

Formula for spacing equal intervals in perspective: the diagonal method. Draw a horizontal baseline, mark equal segments, connect each mark to a single VP, then use a diagonal from the farthest point to the horizon to find the receding spacing.

透视中等距间隔的画法公式：对角线法。画一条水平基线并等分，将各分点与灭点连接，然后从最远点向视平线引一对角线，即可求出后退的等距间隔。

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6. The Golden Ratio (Φ) | 黄金比例

The golden ratio is a proportional relationship found in nature and art. It is defined by dividing a line into two parts so that the ratio of the whole to the longer part equals the ratio of the longer part to the shorter part.

黄金比例是自然界和艺术中出现的一种比例关系。其定义为：将一条线段分成两部分，使整体与较长部分之比等于较长部分与较短部分之比。

(a + b) / a = a / b = Φ ≈ 1.618

If a rectangle’s sides follow this ratio, it is a golden rectangle. Removing a square from it leaves a smaller golden rectangle, creating a logarithmic spiral known as the golden spiral. Many Renaissance paintings and contemporary designs employ Φ to create aesthetically pleasing compositions.

若矩形两边之比满足此值，则为黄金矩形。从中移除一个正方形后，剩下的矩形仍为黄金矩形，重复这一过程可画出对数螺旋，即黄金螺旋。许多文艺复兴时期的绘画和当代设计利用 Φ 创造出赏心悦目的构图。

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7. Rule of Thirds | 三分法则

The rule of thirds divides the image area 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 tends to produce 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面分割成九个相等的矩形。将主体元素放置在这些线或它们的交叉点上，往往比居中构图更具动感和平衡。

Formula: If the picture’s width is W and height is H, draw lines at ⅓ W, ⅔ W, ⅓ H and ⅔ H. The four intersection points are the ‘power points’ where the eye is naturally drawn. For landscapes, placing the horizon on the upper or lower third line is often more effective than splitting the frame in half.

公式：若画面宽为 W、高为 H，分别在 ⅓ W、⅔ W、⅓ H 和 ⅔ H 处画线。四个交点为“趣味中心”，眼睛天然会被这些位置吸引。在风景画中，将地平线放在上方或下方的三分线上，通常比将画面平分成两半更有效。

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8. Human Figure Proportions | 人体比例

Classical canon holds that an ideal adult human figure is about 7.5 to 8 heads tall. The proportions can be expressed as a set of simple relations:

古典标准认为理想成人身高约为 7.5 到 8 个头高。比例可用一组简单关系表示：

• Head length = 1 unit
• 从头顶到下巴 = 1 个单位
• Shoulder width ≈ 2 head widths (for males, slightly narrower for females)
• 肩宽 ≈ 2 个头宽（男性，女性略窄）
• Elbow falls at the waist, roughly at the 3‑head mark from the top
• 肘部位于腰部，约从头顶向下 3 个头长处
• Wrist reaches mid‑thigh, around 4 heads down
• 手腕到大腿中部，约 4 个头长处
• Fingertips extend to mid‑thigh or just above the knee
• 指尖伸展到大腿中部或膝盖稍上方
• Total height = 7.5–8 heads
• 总身高 = 7.5–8 个头长

These ratios vary with age and style, but they provide a reliable starting framework for figure drawing. Leonardo da Vinci’s Vitruvian Man illustrates how the navel acts as the centre of a circle and how limbs relate to geometric proportion.

这些比例随年龄和风格而变化，但为人物画提供了可靠的参考框架。达芬奇的《维特鲁威人》展示了肚脐如何作为圆的中心，以及四肢如何与几何比例相关。

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9. Line Language and Emotional Impact | 线条语言与情感影响

Different line directions and qualities evoke specific psychological responses. These ‘line theorems’ help artists control mood and movement:

不同的线条方向和质感会引发特定的心理反应。以下“线条定理”有助于艺术家控制情绪和动感：

Horizontal lines suggest calmness, rest and stability, mirroring the horizon. Vertical lines convey strength, height and formality, like standing figures or pillars. Diagonal lines express action, tension and dynamism because they are visually unstable. Curved lines imply softness, grace and organic flow. Jagged, zigzag lines communicate anxiety, energy or conflict.

水平线暗示平静、休息和稳定，如同地平线。垂直线传达力量、高度和正式感，如站立的人像或柱子。对角线因视觉上的不稳定性而表现出动感、紧张和活力。曲线蕴含着柔和、优雅与有机流动。锯齿状线条传达焦虑、能量或冲突。

Combining lines creates complex narratives. For instance, a composition dominated by diagonals with a single vertical anchor can balance energy with stability.

线条组合则创造出复杂的叙事。例如，以对角线为主、穿插一根垂直锚点的构图，可以在活力与稳定间取得平衡。

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10. Value Contrast and Atmospheric Perspective | 明度对比与空气透视

Value describes the lightness or darkness of a tone. The contrast formula defines the relationship between objects and their backgrounds:

明度描述色调的深浅。对比公式定义了物体与背景之间的关系：

High Contrast = Large Value Difference → objects appear closer, more dramatic

Low Contrast = Small Value Difference → objects recede, appear softer

高对比 = 明度差异大 → 物体显近、更具冲击力；低对比 = 明度差异小 → 物体后退、更柔和。

Atmospheric perspective formulas: As objects recede into the distance, their values lighten (or blur), colours cool (shift toward blue‑grey) and edges soften. This mimics the scattering of light by the atmosphere. An artist can create depth by applying the ‘distance = lighter + cooler + softer’ rule.

空气透视公式：物体越远，其明度越亮（或变模糊），色彩变冷（偏蓝灰），边缘变柔和。这模拟了大气散射光的效果。艺术家可运用“距离 = 亮 + 冷 + 柔”的规则营造深度。

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11. Colour Temperature and Spatial Depth | 色温与空间深度

Colour temperature is a powerful spatial formula. Warm hues (red, orange, yellow) appear to advance toward the viewer, while cool hues (blue, green, violet) appear to recede. This is due to the way the eye perceives wavelengths and atmospheric effects.

色温是一种强大的空间公式。暖色相（红、橙、黄）看起来向观者靠近，冷色相（蓝、绿、紫）则显得后退。这与眼睛对波长和大气效应的感知方式有关。

A practical theorem: To increase the illusion of depth, paint foreground elements with warm, high‑saturation colours and strong contrasts, and treat background elements with cool, low‑saturation hues and softer edges. Even within a single colour, a warmer variant advances while a cooler variant recedes.

实用定理：要增强深度感，可用暖色、高饱和度和强对比处理前景，用冷色、低饱和度和柔和边缘处理背景。即使在同一颜色内部，偏暖的变体前进，偏冷的变体后退。

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12. Dynamic Composition with the Golden Spiral | 黄金螺旋与动态构图

Building on the golden ratio, the golden spiral helps arrange elements along a natural flow. The spiral is constructed inside nested golden rectangles by drawing quarter‑circle arcs connecting opposite corners of each square removed.

在黄金比例基础上，黄金螺旋有助于沿自然流动安排元素。该螺旋在嵌套黄金矩形内，通过连接每个移除正方形的对角绘制四分之一圆弧构成。

The resulting curve leads the viewer’s eye from the outer edge toward the focal point at the spiral’s centre, creating a flowing, organic composition. This formula, often seen in the curl of a breaking wave or a nautilus shell, has been used by artists from Hokusai to contemporary photographers. When composing a picture, try aligning the main subject’s centre of interest with the tightest coil of the spiral.

所得曲线引导观者视线从外缘指向螺旋中心的焦点，形成流畅、有机的构图。这一公式常见于海浪卷曲或鹦鹉螺壳中，从葛饰北斋到当代摄影师都曾运用。构图时，可以尝试将主体趣味中心对准螺旋最紧密的线圈。

Published by TutorHao | Art Revision Series | aleveler.com

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