📚 Year 7 CIE Art: Formula & Theorem Quick Reference Handbook | Year 7 CIE 艺术：公式定理速查手册
Art might seem free of rules, but behind every great composition lie fundamental ‘formulas’—the elements and principles of design, colour theory, perspective, and proportion. This quick reference handbook gathers the essential formulas and theorems that Year 7 CIE art students need to know, bridging creativity with structure.
艺术看似无拘无束，但每一幅伟大作品的背后都有基本的“公式”——设计元素与原则、色彩理论、透视与比例。这本速查手册汇集了 Year 7 CIE 艺术学生需要掌握的核心公式和定理，在创意与结构之间架起桥梁。
1. The Elements of Art | 艺术元素
The seven building blocks of art are line, shape, form, space, texture, value, and colour. Every artwork uses at least some of these elements.
艺术的七大基石是线条、形状、形体、空间、质感、明暗和色彩。每一件艺术作品至少运用其中几个元素。
Line – A path created by a moving point. It can vary in width, direction, and length.
线条 – 由移动的点产生的路径。它可以变化宽度、方向和长度。
Shape – A two-dimensional enclosed area, such as circles or squares.
形状 – 二维封闭区域，例如圆形或方形。
Form – A three-dimensional object that has height, width, and depth, like a cube or sphere.
形体 – 具有高度、宽度和深度的三维物体，例如立方体或球体。
Space – The area around, between, or within objects. Positive space is the subject; negative space is the background.
空间 – 物体周围、之间或内部的区域。正空间是主体；负空间是背景。
Texture – The surface quality of an object, whether real (tactile) or implied (visual).
质感 – 物体表面的触觉或视觉品质，可以是真实的或暗示的。
Value – The lightness or darkness of a colour, also called tone.
明暗 – 颜色的明度或暗度，也称为色调。
Colour – Produced when light reflects off an object. Hue, saturation, and brightness define it.
色彩 – 光线从物体上反射时产生的视觉效果。由色相、饱和度和亮度界定。
2. Principles of Design | 设计原则
Principles of design are the ‘formulas’ for organising art elements. They include balance, contrast, emphasis, movement, pattern, rhythm, and unity.
设计原则是组织艺术元素的“公式”，包括平衡、对比、强调、动感、图案、节奏和统一。
Balance – The distribution of visual weight. It can be symmetrical, asymmetrical, or radial.
平衡 – 视觉重量的分布，可以是对称、不对称或放射状的。
Contrast – Placing opposing elements (e.g., light vs dark) next to each other to create interest.
对比 – 将相反元素（如亮与暗）并置以营造趣味。
Emphasis – Creating a focal point that draws the viewer’s eye first.
强调 – 创造吸引观者目光的焦点。
Movement – Guiding the viewer’s eye through the artwork along lines, edges, or colours.
动感 – 用线条、边缘或色彩引导观者的视线在画面中移动。
Pattern – Repeating an element or motif in a predictable way.
图案 – 以可预测的方式重复某个元素或母题。
Rhythm – Creating visual tempo by repeating elements with variation.
节奏 – 通过有变化的重复元素创造视觉节拍。
Unity – All parts of the artwork feeling cohesive and belonging together.
统一 – 作品所有部分感觉凝聚在一起、相辅相成。
3. Colour Wheel Formulas | 色轮公式
The colour wheel is a circular diagram of hues. The basic formula for mixing colours begins with three primary colours.
色轮是色相的圆形图表。调色的基本公式从三原色开始。
Primary + Primary = Secondary
原色 + 原色 = 间色
Primary colours: Red, yellow, and blue. They cannot be made by mixing other colours.
原色：红、黄、蓝。它们无法通过混合其他颜色得到。
Secondary colours: Orange (red + yellow), green (yellow + blue), and violet (blue + red).
间色：橙色（红+黄）、绿色（黄+蓝）和紫色（蓝+红）。
Tertiary colours result from mixing a primary and a secondary colour, e.g., red-orange, yellow-green.
复色由原色与间色混合而成，例如红橙、黄绿。
| English Term | 中文术语 | Mixing Formula |
|---|---|---|
| Red + Yellow | 红+黄 | Orange |
| Yellow + Blue | 黄+蓝 | Green |
| Blue + Red | 蓝+红 | Violet |
4. Colour Harmony Rules | 色彩和谐法则
Colour harmonies are ‘formulas’ for combining colours that look pleasing together. They are based on their positions on the colour wheel.
色彩和谐是将悦目的色彩组合在一起的“公式”，基于它们在色轮上的位置。
Complementary colours: Hue₁ + 180° = Hue₂
互补色：色相₁ + 180° = 色相₂
Complementary colours sit opposite on the wheel, e.g., red and green. They create high contrast.
互补色在色轮上彼此相对，例如红与绿，产生强烈对比。
Analogous colours: Three colours side by side on the wheel, e.g., blue, blue-green, green. They create harmony and unity.
类似色：色轮上相邻的三个颜色，例如蓝、蓝绿、绿。它们营造和谐与统一感。
Triadic colours: Three colours evenly spaced (120° apart), e.g., red, yellow, blue. They offer vibrant balance.
三角色：三个等距（相隔 120°）的颜色，例如红、黄、蓝，形成活泼的平衡。
5. The Rule of Thirds | 三分法构图
The rule of thirds divides an image into nine equal parts using two horizontal and two vertical lines. Placing key elements along these lines or at intersections creates a balanced, dynamic composition.
三分法用两条水平线和两条垂直线将画面平分成九等份。将关键元素放在线条上或交点处能创造出平衡而富有动感的构图。
Focal point ≈ Intersection of 1/3 lines
焦点 ≈ 三分线交点
For a landscape, place the horizon on the upper or lower third line, not dead centre.
画风景时，将地平线放在上方或下方的三分线上，而非正中。
For a portrait, align the subject’s eyes with the upper third line to give the composition breathing space.
画肖像时，将人物的眼睛对齐上方三分线，为构图留出呼吸空间。
6. The Golden Ratio in Art | 艺术中的黄金比例
The golden ratio (φ) appears in nature and classical art. It creates aesthetically pleasing proportions and can be used as a compositional tool.
黄金比例 (φ) 出现在自然与古典艺术中，能创造出赏心悦目的比例，可作为一种构图工具。
φ = (1 + √5) ÷ 2 ≈ 1.618
φ = (1 + √5) ÷ 2 ≈ 1.618
Using a golden spiral or golden rectangle helps guide the viewer’s eye towards the focal area.
使用黄金螺旋或黄金矩形有助于引导观者视线朝向焦点区域。
Many Renaissance paintings used the golden ratio to position figures and architectural elements.
许多文艺复兴绘画使用黄金比例来定位人物和建筑元素。
7. One-Point Perspective Formula | 一点透视公式
One-point perspective uses a single vanishing point on the horizon line. All lines receding into the distance converge at this point.
一点透视在水平线上使用一个消失点，所有往远处延伸的线条都汇聚于该点。
All parallel depth lines → single vanishing point (VP) on horizon
所有平行的纵深线条 → 水平线上的单一消失点 (VP)
Draw the horizon line first, mark the vanishing point, then draw objects with their front faces parallel to the viewer.
先画水平线，标出消失点，然后画出正面平行于观众的物体。
Good for railway tracks, roads, or hallways seen head-on.
适用于正对观众的铁路、道路或走廊。
8. Two-Point Perspective Formula | 两点透视公式
Two-point perspective uses two vanishing points on the horizon line, typically placed far apart. Vertical lines remain vertical; horizontal edges angle towards the respective vanishing point.
两点透视在水平线上使用两个消失点，通常相距较远。垂直线保持垂直；水平边缘则斜向各自的消失点。
Left receding lines → VP₁ ; Right receding lines → VP₂ ; Vertical edges = straight
左后方线条 → 消失点 1；右后方线条 → 消失点 2；垂直棱 = 笔直
Start with the nearest vertical edge of the object; connect its top and bottom to both vanishing points.
从物体最近的垂直棱开始，将其上下端分别连向两个消失点。
Ideal for drawing a building seen from a corner or an open book.
非常适合绘制从角落看到的建筑或打开的书本。
9. Shading and Tone: Value Scale Formula | 明暗与色调：明度等级公式
A value scale shows the gradual transition from white to black through a series of greys. It helps artists control contrast and form.
明度等级展示了从白到黑通过一系列灰色渐变的过渡，帮助艺术家掌控对比和形体。
Value step = (Max value − Min value) ÷ Number of steps
明度间隔 = (最大明度 − 最小明度) ÷ 步数
A typical 5-step scale: White, light grey, mid grey, dark grey, black. Blending between steps creates smooth form.
典型的五级明度：白、浅灰、中灰、深灰、黑。在各步之间进行调和可以塑造柔和的形体。
Shading techniques include hatching, cross-hatching, stippling, and blending. The direction of light determines highlight, mid-tone, and shadow.
明暗技法包括排线、交叉排线、点画和调和。光线的方向决定了高光、中间调和阴影。
10. Portrait Proportion Guidelines | 肖像比例指南
Facial proportions follow predictable ‘formulas’ that help beginners draw realistic portraits. These guidelines apply to a front-facing, average human face.
面部比例遵循可预测的“公式”，帮助初学者画出逼真的肖像。这些准则适用于正面的正常人脸。
Eye line = Halfway down the head (from crown to chin)
眼睛线 = 头顶到下巴的一半
The head shape is roughly an upside-down oval. The eyes are aligned on the horizontal halfway line; the width between them equals one eye length.
头型大致是一个倒置的椭圆形。双眼对齐水平中线；两眼之间的距离等于一只眼睛的长度。
Nose bottom line = halfway between eye line and chin. Mouth line = halfway between nose bottom and chin.
鼻底线 = 眼睛线与下巴之间的中点。嘴唇线 = 鼻底与下巴之间的中点。
Ears align with the brow line and the nose bottom line. Hairline begins about a quarter to a third down from the crown.
耳朵对齐眉线与鼻底线。发际线从头顶起约四分之一到三分之一处开始。
11. Pattern and Rhythm | 图案与节奏
Pattern repeats a single motif regularly, while rhythm uses repeated elements with variation to create visual movement, like a beat in music.
图案以一种单一母题进行规律重复，而节奏则通过有变化的重复元素创造视觉运动，宛如音乐中的节拍。
Rhythm = Repetition + Variation
节奏 = 重复 + 变化
Types of visual rhythm: regular (even spacing), flowing (curved, organic), progressive (changing size or shape), and alternating.
视觉节奏的类型：规律的（等距）、流动的（曲线、有机）、渐进的（大小或形状变化）和交替的。
Pattern can be found in textile design, nature (leaf arrangements), and abstract art. It brings order and can also energise a surface.
图案见于纺织品设计、自然（叶片排列）和抽象艺术中。它能带来秩序感，也能为画面增添活力。
12. Balance in Composition | 构图平衡
Balance refers to how visual weight is distributed. The three main formulas are symmetrical, asymmetrical, and radial balance.
平衡指视觉重量的分布方式。三种主要公式为对称平衡、不对称平衡和放射平衡。
Visual weight = size × contrast × colour intensity × position
视觉重量 = 大小 × 对比度 × 色彩强度 × 位置
Symmetrical balance (formal): mirror image along a central axis, conveying stability and calm.
对称平衡（正式）：沿中轴的镜像，传达稳定与宁静。
Asymmetrical balance (informal): different elements of equal visual weight, creating dynamic tension.
不对称平衡（非正式）：视觉重量相等的不同元素，产生动态张力。
Radial balance: elements arranged around a central point, like the petals of a flower, leading the eye inward.
放射平衡：元素围绕中心点排列，如同花瓣，将视线引向中心。
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