Year 7 CAIE Art: Essential Formulas and Theorems Quick Reference | 艺术基础公式定理速查手册

📚 Year 7 CAIE Art: Essential Formulas and Theorems Quick Reference | 艺术基础公式定理速查手册

Art may seem to be a world of pure creativity and free expression, but behind every successful composition there are clear principles, formulas and theorems that guide the artist’s hand. From colour mixing equations to the laws of perspective, these ‘rules’ are the grammar of visual language. This quick reference handbook collects the essential artistic formulas and theorems for Year 7 CAIE Art students, providing a structured foundation to support your creative practice and analytical thinking.

艺术或许像是一个纯粹创造力与自由表达的世界，但在每一件成功作品的背后，都有一套明确的原则、公式和定理在指引着艺术家的双手。从色彩混合方程式到透视法则，这些“规则”正是视觉语言的语法。这本速查手册汇集了为 Year 7 CAIE 艺术学生准备的核心艺术公式与定理，为你提供一个结构化的基础，以支持你的创作实践与分析思维。

1. The Primary Colour Formula | 三原色公式

In pigment-based art, the three primary colours are red, yellow and blue. These cannot be created by mixing other colours. They form the basis of all other hues.

在颜料艺术中，三原色是红、黄、蓝。它们无法通过混合其他颜色得到，是一切色调的基础。

Formula: Primary = {Red, Yellow, Blue}

公式: 原色 = {红, 黄, 蓝}

Red, yellow and blue are the irreducible building blocks of the colour wheel.
红、黄、蓝是色轮上不可再分解的构建模块。
Every other colour you see can be traced back to a mixture of these three.
你看到的其他任何颜色都可以追溯到这三种原色的混合。

2. Secondary Colour Mixing Equations | 二次色混合方程式

Secondary colours are created by mixing two primary colours in equal amounts. The formulas are precise and reliable.

二次色由两种原色等量混合而成。这些方程式精确且可靠。

Red + Yellow = Orange

红 + 黄 = 橙

Yellow + Blue = Green

黄 + 蓝 = 绿

Blue + Red = Violet (Purple)

蓝 + 红 = 紫

Orange, green and violet complete the six major divisions of the basic colour wheel.
橙、绿、紫构成了基础色轮上的六大主要分区。
Adjusting the ratio of the two primaries will produce intermediate, or tertiary, hues.
调整两种原色的比例会产生中间色，即三次色。

3. Tertiary Colour Theorem | 三次色定理

When a primary colour is mixed with an adjacent secondary colour, six tertiary colours are formed. These fill the gaps on the colour wheel and are named by combining the two parent colours, always listing the primary first.

当一种原色与相邻的二次色混合时，便形成了六种三次色。它们填补了色轮上的空隙，以两种母色命名，并且始终将原色放在前面。

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

Tertiary colours give artists a wider spectrum for subtle colour harmonies and realistic rendering.
三次色为艺术家提供了更广的光谱，有利于实现微妙的色彩和谐与写实表现。

4. Complementary Colour Theorem | 互补色定理

Complementary colours are those positioned directly opposite each other on the colour wheel. When placed side by side, they create maximum contrast and visual vibration. When mixed together, they neutralise each other, producing a grey or brown tone.

互补色是色轮上正对位置的颜色。当它们并置时，能产生最大的对比度与视觉振动。当混合在一起时，它们会相互中和，产生灰色或棕色。

Colour	Complementary	颜色	互补色
Red	Green	红	绿
Yellow	Violet	黄	紫
Blue	Orange	蓝	橙

Use complements to make a subject stand out: a red apple on a green cloth appears more vibrant.
使用互补色可让主体更突出：红苹果放在绿布上显得更鲜艳。
Mixing complements is the secret to creating realistic shadows, as pure black often looks unnatural.
混合互补色是创造逼真阴影的秘诀，因为纯黑色往往看起来不自然。

5. Value and Tint/Shade Formula | 明度与调子公式

Value refers to how light or dark a colour is. By adding white or black, you can systematically alter a colour’s value without changing its hue.

明度指颜色的明暗程度。通过添加白色或黑色，你可以有条理地改变颜色的明度而不改变其色相。

Tint = Hue + White

亮调 = 纯色 + 白

Shade = Hue + Black

暗调 = 纯色 + 黑

Tone = Hue + Grey (Black + White)

灰调 = 纯色 + 灰 (黑 + 白)

A value scale typically has 9 steps from white to black; a colour value scale shows the transitions of a single hue.
明度标尺通常从白到黑分为9级；彩色明度标尺则展示单一色相的过渡。
Value creates the illusion of form. High value contrast can bring objects forward, while low contrast pushes them back.
明度能够创造形体的幻觉。高明度对比可将物体拉近，低对比度则使其后退。

6. One-Point Perspective Rule | 一点透视法则

One-point perspective is a geometric system for representing three-dimensional space on a two-dimensional surface. All receding parallel lines converge at a single vanishing point on the horizon line.

一点透视是一种在二维平面上表现三维空间的几何系统。所有后退的平行线都会汇聚于地平线上的一个消失点。

Rule: All depth lines → Vanishing Point (VP) on Horizon Line

法则: 所有纵深线 → 消失点 (VP) 在地平线上

Front-facing planes remain undistorted, drawn as true rectangles or squares.
正对观者的平面保持不变形，绘制为真实的矩形或正方形。
Use this for roads, railway tracks, corridors, or any scene where the viewer looks straight ahead.
适用于道路、铁轨、走廊或任何直接向前看的场景。
Objects become smaller as they approach the vanishing point, following the law of diminishing size.
物体越靠近消失点就变得越小，遵循近大远小的规律。

7. Two-Point Perspective Theorem | 两点透视定理

When a corner of an object faces the viewer, two sets of parallel lines recede to two separate vanishing points on the horizon. This creates a more dynamic and realistic sense of depth.

当物体的一个角面向观者时，两组平行线分别后退到地平线上的两个不同消失点。这能营造出更动感、更真实的空间深度感。

Theorem: Left receding lines → VP1; Right receding lines → VP2

定理: 左侧后退线 → VP1; 右侧后退线 → VP2

Both vanishing points must lie on the same horizon line.
两个消失点必须位于同一条地平线上。
Vertical lines remain vertical, parallel to the edges of the paper.
垂直线保持垂直，与画面边缘平行。
Use for buildings seen at an angle, furniture, or any box-like forms not directly facing the eye.
适用于成角度的建筑、家具或任何不正面朝向眼睛的盒状形态。

8. The Rule of Thirds: Composition Grid | 三分法则：构图网格

The rule of thirds divides the picture plane into nine equal rectangles with two horizontal and two vertical lines. Placing key elements along these lines or at their intersections creates a balanced, engaging composition.

三分法则用两条水平线和两条垂直线将画面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点上，能创造出平衡且引人入胜的构图。

Focal Point Position = Intersections of Thirds Lines

焦点位置 = 三分线的交点

Horizons should generally sit on the upper or lower third line, not the exact middle, unless reflecting symmetry.
地平线通常应放置在上方或下方的三分线上，而非正中央，除非意在表现对称。
Main subjects gain impact when placed on the left or right vertical third line.
主要对象放在左侧或右侧的垂直三分线时能获得更强的冲击力。
Our eyes naturally gravitate to these intersection points, making the rule a powerful compositional tool.
我们的眼睛会自然地移向这些交点，使得这一法则成为强有力的构图工具。

9. The Golden Ratio (Divine Proportion) Formula | 黄金比例 (神圣比例) 公式

Found in nature, architecture and classical art, the golden ratio is an irrational number approximately equal to 1.618. When applied to composition, it creates a spiral or rectangle of harmonious proportions.

黄金比例存在于自然、建筑和古典艺术中，它是一个约等于 1.618 的无理数。当运用于构图时，它会形成和谐比例的螺旋线或矩形。

φ = (1 + √5) / 2 ≈ 1.618

φ = (1 + √5) ÷ 2 ≈ 1.618

A golden rectangle has side ratio a : b = 1 : 1.618. Removing a square from it leaves another golden rectangle.
黄金矩形的边长比 a : b = 1 : 1.618。从中移除一个正方形后，剩余部分仍然是黄金矩形。
Draw a golden spiral by connecting arcs through the squares of a golden rectangle.
连接黄金矩形内部各正方形的弧线就可画出黄金螺旋线。
Place your focal point at the heart of the spiral, and arrange secondary elements along the curve for a naturally graceful flow.
将焦点放在螺旋线的中心，并沿曲线安排次要元素，可获得自然而优美的流动感。

10. The Human Body Proportion Canon | 人体比例法则

Artists use an idealised system of measurement to draw the human figure. The classical canon uses the head as the basic unit: the average adult body is about 7.5 to 8 heads tall.

艺术家使用理想化的测量系统来绘制人体。古典法则以头部为基本单位：成人的身体大约为 7.5 到 8 个头高。

Body Height = 8 × Head Height (Ideal Canon)

身体高度 = 8 × 头高 (理想法则)

Landmark	Approx. Head Unit	标志点	头长单位
Chin	0	下巴	0
Nipples	2	乳头	2
Navel	3	肚脐	3
Hips/Pubic bone	4	髋部/耻骨	4
Fingertips	5	指尖	5
Knees	6	膝盖	6
Soles of feet	8	脚底	8

Arms extended horizontally match the total body height (Vitruvian principle).
水平伸开的双臂长度相当于全身高度 (维特鲁威原理)。
These proportion rules help you construct figures that look plausible and well-balanced.
这些比例规则帮助你构建看起来合理且比例协调的人物。

11. Chiaroscuro: The Light and Shadow Theorem | 明暗对比定理

Chiaroscuro is the technique of using strong contrasts between light and dark to create the illusion of volume and depth. The core elements are highlight, midtone, core shadow, reflected light and cast shadow.

明暗对照法是一种利用强烈光影对比来创造立体感和深度感的技法。其核心要素包括高光、中间调、明暗交界线、反光和投影。

Volume Illusion = Highlight + Midtone + Core Shadow + Reflected Light + Cast Shadow

立体错觉 = 高光 + 中间调 + 明暗交界线 + 反光 + 投影

The core shadow is the darkest area on the object itself, sitting between the light side and the reflected light.
明暗交界线是物体自身最暗的区域，位于亮面与反光之间。
Cast shadows anchor the object to a surface and reveal the direction and intensity of the light source.
投影使物体固定于表面，并揭示光源的方向与强度。
Gradual blending of tones softens the transition and makes spherical and organic forms look rounded.
柔和的色调过渡能使球体和有机形态显得圆润。

12. Atmospheric Perspective Formula | 空气透视公式

Atmospheric perspective describes how distance affects the appearance of objects. As objects recede into the distance, they lose contrast, become lighter in value, cooler in colour temperature, and blurrier in edge sharpness.

空气透视描述了距离如何影响物体的外观。当物体向远处退去时，它们会失去对比度、明度变亮、色温变冷、边缘清晰度变得模糊。

Distance → ↓Contrast + ↑Value (Lighter) + Cooler Hues + Softer Edges

距离 → ↓对比度 + ↑明度 (更亮) + 偏冷色调 + 柔和边缘

Foreground: strong darks and lights, rich warm colours, sharp outlines.
前景: 强烈的深色与亮色、丰富的暖色、清晰的轮廓。
Middle ground: moderate contrast, neutralised hues.
中景: 中等对比度、中性化的色调。
Background: low contrast, pale blues or greys, almost no detail.
远景: 低对比度、浅淡的蓝色或灰色、几乎没有细节。
This formula is essential for landscape painting and any work depicting deep space.
这一公式对于风景画和任何表现深远空间的作品都至关重要。

Published by TutorHao | Art Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Year 7 CAIE Art: Essential Formulas and Theorems Quick Reference | 艺术基础公式定理速查手册