📚 Year 7 CIE Art: Formula & Theorem Quick Reference Handbook | 7年级CIE艺术：公式定理速查手册
In art, there are no mathematical formulas with absolute answers, but there are fundamental rules and visual principles that act like laws of nature. These art 'formulas' help young artists understand how colours mix, how perspective works, and how to create balanced compositions. This quick reference handbook summarises the key theorems and formulas you need for Year 7 CIE Art.
在艺术中，并没有像数学那样得出绝对答案的公式，但有一些基本规则和视觉原理，它们就像自然法则一样起作用。这些艺术“公式”能帮助小艺术家们理解颜色如何混合、透视如何运作，以及如何创作平衡的构图。这本速查手册总结了7年级CIE艺术所需的关键定理与公式。
1. Colour Wheel Basics | 色轮基础
The colour wheel arranges hues in a circle to show relationships. Primary colours are red, yellow, and blue. Secondary colours are made by mixing two primary colours. Tertiary colours result from mixing a primary with a secondary colour.
色轮将各种色相排列成一个圆圈，以展示它们之间的关系。原色是红、黄、蓝。间色由两种原色混合而成。复色则由一种原色与一种间色混合得到。
Red + Yellow = Orange
Yellow + Blue = Green
Blue + Red = Purple (Violet)
These formulas are the starting point for all colour mixing.
这些公式是所有色彩混合的起点。
| Primary | Red, Yellow, Blue |
| 原色 | 红、黄、蓝 |
| Secondary | Orange, Green, Purple |
| 间色 | 橙、绿、紫 |
| Tertiary examples | Red-Orange, Yellow-Green, Blue-Purple |
| 复色例子 | 红橙、黄绿、蓝紫 |
2. Primary, Secondary & Tertiary Colours | 原色、间色与复色
Primary colours cannot be created by mixing other paints. They are the pure building blocks. Secondary colours are the children of two primaries. Tertiary colours fill the gaps on a 12-colour wheel.
原色无法通过混合其他颜料得到，它们是纯粹的基石。间色是两种原色混合后产生的“孩子”。复色填充了12色轮上的空隙。
Primary + Primary → Secondary
Primary + Secondary → Tertiary
For example, mixing red (primary) and orange (secondary) yields red-orange, a tertiary colour.
例如，将红色（原色）与橙色（间色）混合，就得到红橙，一种复色。
Tertiary colour names always start with the primary hue first: yellow-green, blue-green, blue-purple, red-purple, red-orange, yellow-orange.
复色的命名总是把原色放在前面：黄绿、蓝绿、蓝紫、红紫、红橙、黄橙。
3. Colour Harmonies & Formulas | 色彩调和公式
Colour harmonies are planned combinations that are pleasing to the eye. Artists use these 'recipes' to create mood and unity.
色彩调和是经过计划、令人赏心悦目的色彩组合。艺术家使用这些“配方”来营造氛围与统一感。
Complementary Formula: Opposite colours on the wheel (180° apart) = maximum contrast
互补公式：色轮上相对（相隔180°）的颜色 = 最大对比
Examples: Red + Green, Blue + Orange, Yellow + Purple. When mixed, they neutralise each other to create browns and greys.
例子：红 + 绿，蓝 + 橙，黄 + 紫。当它们混合时，会相互中和产生棕色和灰色。
Analogous Formula: 3 neighbouring colours = harmony with low contrast
类似色公式：3种相邻的颜色 = 低对比的和谐
Example: Yellow, Yellow-Green, Green. Analogous schemes are often found in nature.
例子：黄、黄绿、绿。类似色方案常出现在自然界中。
Triadic Formula: 3 colours evenly spaced (120° apart) = vibrant balance
三角色公式：3种均匀分布（间隔120°）的颜色 = 充满活力的平衡
Example: Red, Yellow, Blue (the primaries) or Orange, Green, Purple.
例子：红、黄、蓝（原色）或橙、绿、紫。
4. Warm vs Cool Colours | 暖色与冷色
The colour wheel can be split into warm and cool halves. This temperature theory helps create depth and emotion.
色轮可分为暖色半区和冷色半区。这种温度理论有助于创造深度和情感。
Warm colours: Red through Yellow-Green → advance, energetic
暖色：从红到黄绿 → 前进感、充满能量
Cool colours: Green through Red-Violet → recede, calm
冷色：从绿到红紫 → 后退感、宁静
In a landscape, distant mountains often appear cooler and bluer due to atmospheric perspective. Artists use this formula: warm foreground, cool background.
在风景画中，远处的山往往因为空气透视而显得更冷、更蓝。艺术家利用这个公式：暖色前景，冷色背景。
5. Value, Tint & Shade | 明度、浅色与深色
Value refers to how light or dark a colour is. Adding white, black, or grey changes the value and creates new variations.
明度指颜色的深浅程度。加入白、黑或灰会改变明度并创造新的变体。
Tint = Hue + White
浅色 = 色相 + 白
Shade = Hue + Black
深色 = 色相 + 黑
Tone = Hue + Grey (or adding both white and black)
色调 = 色相 + 灰（或同时加入白与黑）
Understanding value is essential for creating form and depth. A monochromatic painting uses only one hue plus its tints, shades and tones.
理解明度对于表现形体和深度至关重要。单色画仅使用一种色相及其浅色、深色与色调。
6. Line as an Element | 线条元素
Line is the most basic element of art. Different line directions and qualities communicate specific feelings and movement. These can be seen as expressive formulas.
线条是最基本的艺术元素。不同的线条方向与质感传达出特定的感觉和动势。这些可以看作表现力的公式。
Horizontal line = rest, calm, stability
水平线 = 静止、平静、稳定
Vertical line = strength, height, dignity
垂直线 = 力量、高度、庄重
Diagonal line = movement, tension, action
对角线 = 运动、张力、动态
Curved line = softness, flow, natural form
曲线 = 柔和、流动、自然形态
Zigzag line = excitement, chaos, energy
锯齿线 = 兴奋、混乱、能量
Varying line weight (thick vs thin) can also create emphasis and depth. Thick lines come forward, thin lines recede.
改变线条的粗细也能创造强调和深度。粗线显得靠前，细线显得后退。
7. Shape and Form | 形状与形体
Shape is a two-dimensional area with boundaries. Form is a three-dimensional object with volume. The relationship between them follows a clear transformation formula.
形状是有边界的二维区域。形体是具有体积的三维物体。它们之间的关系遵循清晰的转换公式。
Shape + Shading + Perspective → Form
形状 + 明暗 + 透视 → 形体
| 2D Shape | 3D Form |
| Circle (圆形) | Sphere (球体) |
| Square (正方形) | Cube (立方体) |
| Triangle (三角形) | Cone or Pyramid (圆锥或棱锥) |
| Rectangle (长方形) | Cylinder or Rectangular Prism (圆柱或长方体) |
Geometric shapes are precise and regular; organic shapes are irregular and found in nature. Both can be developed into forms.
几何形状精确而规则；有机形状不规则，常见于自然界。两者都能发展为形体。
8. One-Point Perspective | 一点透视法
One-point perspective is a drawing method that creates the illusion of depth on a flat surface. All receding parallel lines converge at a single vanishing point on the horizon line.
一点透视是一种在平面上创造深度错觉的绘图方法。所有后退的平行线都汇聚于视平线上的一个消失点。
Horizon Line (HL) + Vanishing Point (VP) + Orthogonal Lines = Depth
视平线 + 消失点 + 正交线 = 深度
The front face of an object remains flat and parallel to the picture plane. Side faces recede toward the VP. Use this formula when drawing roads, railway tracks, or corridors.
物体的正面保持平坦并与画面平行。侧面则向消失点后退。绘制道路、铁轨或走廊时使用此公式。
Example: a cube in one-point perspective has its front face as a true square, while the top, bottom, and side edges all converge to the single VP.
例子：一点透视中的立方体正面是真实的正方形，而顶部、底部和侧面的边都汇聚到同一个消失点。
9. Two-Point Perspective | 两点透视法
Two-point perspective is used when the corner of an object faces the viewer. Two vanishing points are placed on the horizon line, and vertical lines remain vertical.
当物体的角朝向观者时使用两点透视。两个消失点位于视平线上，所有垂直线保持垂直。
2 VPs on Horizon Line + Vertical edges = 3D corner view
视平线上2个消失点 + 垂直边 = 三维转角视图
All edges except the vertical ones aim toward either VP1 (left) or VP2 (right). This formula is essential for drawing buildings viewed from an angle.
除垂直边外，所有边缘都指向左侧消失点或右侧消失点。这个公式对于绘制从某个角度观看的建筑至关重要。
Remember: the closer the vanishing points are to each other, the more extreme the perspective distortion. Placing them far apart creates a more natural look.
请记住：两个消失点越靠近，透视畸变越强烈。将它们放远一些，会得到更自然的效果。
10. Rule of Thirds Composition | 三分法构图
The Rule of Thirds is a composition guideline that divides the picture plane into nine equal parts using two horizontal and two vertical lines. The four intersection points become focal 'hotspots'.
三分法是一种构图指南，用两条水平线和两条垂直线将画面分成九个相等部分。四个交叉点成为视觉焦点“热点”。
Key elements placed on intersections or along the lines = dynamic, balanced composition
将关键元素放在交叉点或线条上 = 动态、平衡的构图
Placing the horizon on the upper or lower third line (instead of centre) often produces a more interesting landscape. A subject placed at a right or left intersection feels more engaging than dead centre.
将视平线放在上方或下方的三分之一线上（而非正中间），通常会产生更有趣的风景画。主体放在右侧或左侧的交叉点上，比放在正中央更吸引人。
11. Golden Ratio & Proportion | 黄金比例与比例
The Golden Ratio (approximately 1.618) has been used in art and architecture for centuries to create aesthetically pleasing proportions. It is often represented by the Greek letter φ (phi).
黄金比例（约1.618）在艺术与建筑中已使用了数个世纪，用来创造悦目的比例。它通常用希腊字母 φ 表示。
a / b = (a + b) / a ≈ 1.618
a / b = (a + b) / a ≈ 1.618
In composition, the Golden Rectangle (where the ratio of the long side to the short side is φ) and the Golden Spiral guide the placement of focal points. Many famous artworks, from the Parthenon to Leonardo da Vinci's 'Vitruvian Man', use this formula.
在构图中，黄金矩形（长边与短边之比为 φ）和黄金螺旋可引导焦点的位置。从帕台农神庙到列奥纳多·达·芬奇的《维特鲁威人》，许多著名作品都运用了这一公式。
Even a simple rule: a division roughly 5:8 approximates the Golden Ratio and can be easily applied by young artists.
即使是一个简单的规则：大约5:8的分割近似于黄金比例，小艺术家们可以轻松运用。
12. Balance & Symmetry | 平衡与对称
Balance refers to the visual weight distribution in an artwork. It can be symmetrical, asymmetrical, or radial. Each type follows a distinct formula.
平衡指艺术作品中视觉重量的分布。它可以是对称的、不对称的或径向的。每种类型遵循不同的公式。
Symmetrical Balance = mirror image across a central axis → formal, calm
对称平衡 = 沿中轴的镜像 → 正式、平静
Asymmetrical Balance = different elements with equal visual 'weight' → dynamic, informal
不对称平衡 = 不同元素具有相等的视觉“重量” → 动态、非正式
Radial Balance = elements radiate from a central point → unity, movement
径向平衡 = 元素从中心点向外辐射 → 统一、动感
Visual weight can be increased by larger size, brighter colour, high contrast, or complex texture. A small dark shape can balance a large light area.
更大的尺寸、更亮的颜色、高对比度或复杂的肌理可以增加视觉重量。一个小的深色形状可以与一个大的浅色区域取得平衡。
These formulas are the invisible mathematics behind a well-composed image.
这些公式正是一幅构图良好的画面背后无形的数学。
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