Year 9 CIE Art: Quick-Reference Guide to Principles & Formulas | Year 9 CIE 艺术：公式定理速查手册

📚 Year 9 CIE Art: Quick-Reference Guide to Principles & Formulas | Year 9 CIE 艺术：公式定理速查手册

Art may not have equations in the traditional sense, but every successful composition relies on repeatable visual ‘formulas’ and proven principles. This handbook collects the essential colour-mixing equations, compositional ratios, perspective rules, and design theorems that Year 9 CIE Art students need to recall when building a portfolio. Mastery of these concepts turns intuitive mark-making into confident, analytical image construction.

艺术或许没有传统意义上的方程式，但每一幅成功的作品都依赖于可重复的视觉“公式”和经过验证的原理。本手册汇集了 Year 9 CIE 艺术学生在构建作品集时需要回忆的基本色彩混合方程、构图比例、透视规则和设计定理。掌握这些概念能将直觉性的涂抹转化为自信、分析的图像构建。

1. Additive Colour Mixing Formulas | 加色混合公式

When working with light (digital screens, stage lighting), the primary colours are red, green, and blue (RGB). Combining two primaries at full intensity produces a secondary colour according to a fixed equation.

在处理光（数字屏幕、舞台灯光）时，三原色是红、绿、蓝 (RGB)。将两种原色以最大强度混合，会按照固定公式产生间色。

Equation (英文)	Equation (中文)	Result Colour
Red + Green → Yellow	红 + 绿 → 黄	Yellow 黄
Green + Blue → Cyan	绿 + 蓝 → 青	Cyan 青
Blue + Red → Magenta	蓝 + 红 → 品红	Magenta 品红
Red + Green + Blue → White	红 + 绿 + 蓝 → 白	White 白

Understanding this additive system helps you predict how coloured lights will blend in installations or when analysing digital art.

了解这个加色系统有助于你在装置艺术或分析数码作品时，预测彩色灯光将如何混合。

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2. Subtractive Colour Mixing & Pigment Formulas | 减色混合与颜料公式

For painting, printing, and drawing, the subtractive primaries are cyan, magenta, and yellow (CMY). In practice, artists often use the traditional primaries red, yellow, and blue (RYB), which yield slightly different mixtures.

对于绘画、印刷和素描来说，减色三原色是青、品红和黄 (CMY)。在实践中，艺术家常使用传统的红、黄、蓝 (RYB)，它们会产生略有不同的混合物。

• RYB mixing equations: Yellow + Blue → Green; Red + Yellow → Orange; Red + Blue → Violet.
• RYB 混合公式： 黄 + 蓝 → 绿；红 + 黄 → 橙；红 + 蓝 → 紫。
• Tint formula: Hue + White → Tint (higher value).
• 色调公式： 色相 + 白 → 浅色调（明度提高）。
• Shade formula: Hue + Black → Shade (lower value).
• 暗调公式： 色相 + 黑 → 暗调（明度降低）。
• Tone formula: Hue + Grey (or complement) → Tone (reduced saturation).
• 浊调公式： 色相 + 灰（或补色） → 浊调（饱和度降低）。

Memorising these relationships gives you control over every mixture on your palette.

记住这些关系，你就能掌控调色板上的每一种混合物。

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3. The Golden Ratio φ as a Compositional Formula | 构图黄金比 φ 公式

The golden ratio, an irrational number approximately equal to 1.618, appears in nature and classical art. Artists have used it to place focal points and divide their canvas for centuries.

黄金比是一个约等于 1.618 的无理数，出现在自然界与古典艺术中。几个世纪以来，艺术家一直用它来放置焦点和分割画面。

φ = (1 + √5) / 2 ≈ 1.618

To apply it, divide your canvas width or height by 1.618 to find the harmonic division point. For example, on a 30 cm side, 30 ÷ 1.618 ≈ 18.54 cm locates a natural resting place for the main subject.

若要应用它，将画布的宽度或高度除以 1.618 即可找到和谐的分割点。例如，在 30 厘米的边上，30 ÷ 1.618 ≈ 18.54 厘米处就是放置主体的自然位置。

The golden spiral, constructed from rotating squares following the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, …), can guide the viewer’s eye through a composition.

黄金螺旋根据斐波那契数列 (1, 1, 2, 3, 5, 8, 13, …) 的旋转正方形构建而成，可引导观者视线穿过构图。

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4. The Rule of Thirds: Simple Grid Formula | 三分法则：简单网格公式

The rule of thirds divides the frame into a 3×3 grid. The formula places points of interest at any of the four intersections where the grid lines cross.

三分法则将画面划分为 3×3 网格。该公式将兴趣点放置在网格线交叉的四个交汇处之一。

If the canvas width is W and height is H, the intersection coordinates are at (W/3, H/3), (2W/3, H/3), (W/3, 2H/3), and (2W/3, 2H/3).

如果画布宽度为 W，高度为 H，交汇点的坐标位于 (W/3, H/3)、(2W/3, H/3)、(W/3, 2H/3) 和 (2W/3, 2H/3)。

Horizons aligned with the upper or lower third line create a more dynamic landscape than dead centre. This quick check can rescue a static composition.

与完全居中相比，将地平线对准上方或下方的三分之一线能创造更富动感的风景画。这项快速检查可以挽救呆板的构图。

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5. Linear Perspective Formulas: One-Point & Two-Point | 线性透视公式：一点与两点透视

Perspective creates the illusion of depth on a flat surface. The central formula for one-point perspective is that all receding parallel lines converge at a single vanishing point (VP) on the horizon line (HL).

透视在平面上创造深度错觉。一点透视的核心公式是所有后退的平行线都汇聚于地平线 (HL) 上的单一消失点 (VP)。

For two-point perspective, edges recede to two separate vanishing points, VP₁ and VP₂, both on the horizon line. The vertical edges of the object remain truly vertical.

对于两点透视，边缘分别向后汇聚到两个消失点 VP₁ 和 VP₂，两者都在地平线上。物体的垂直边缘保持真正的竖直。

As objects move further from the viewer, their apparent size decreases according to the geometric relationship: apparent height ∝ 1/distance. Sketch this repeatedly until it becomes muscle memory.

当物体远离观者时，其表观尺寸根据几何关系减小：表观高度 ∝ 1/距离。反复绘制，直到成为肌肉记忆。

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6. Value Contrast & Luminosity Formulas | 明度对比与亮度公式

Value describes how light or dark a colour appears on a grey scale from 0 (black) to 10 (white). Strong value contrast makes a focal point pop. The formula for high contrast is to place a light shape directly against a dark shape.

明度描述颜色在 0（黑）到 10（白）的灰阶上呈现的明暗程度。强烈的明度对比能让焦点突出。高对比度的公式是直接将浅色形状放在深色形状之上。

A mid-grey surround can alter perception: a mid-grey square appears lighter against black, darker against white – this is simultaneous contrast. Use it intentionally.

中灰色环境会改变感知：一个中灰色方块在黑色背景下显得更亮，在白色背景下显得更暗——这就是同时对比。有意识地运用它。

Chiaroscuro, meaning light-dark in Italian, applies the formula: deep shadow → transitional mid-tones → bright highlight to model three-dimensional form.

Chiaroscuro（意大利语意为明暗）应用公式：深阴影 → 过渡中间调 → 明亮高光，以塑造三维形体。

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7. Compositional Balance Theorem | 构图平衡定理

Visual balance resembles a seesaw. The theorem states that a composition feels stable when the visual weight on either side of a central vertical axis is perceived as equal.

视觉平衡类似于跷跷板。该定理指出，当中央垂直轴两侧的视觉重量感觉相等时，构图就会感到稳定。

Visual weight depends on size, colour intensity, contrast, and detail. A small, high-contrast red shape can balance a large, low-saturation blue shape.

视觉重量取决于尺寸、色彩强度、对比度和细节。一个小的、高对比度的红色形状可以平衡一个大的、低饱和度的蓝色形状。

Symmetrical balance (formal) uses the same elements mirrored, while asymmetrical balance (informal) uses different elements of equal weight. Both follow the weight equation.

对称平衡（正式）使用镜像的相同元素，而非对称平衡（非正式）使用同等重量的不同元素。两者都遵循重量等式。

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8. Negative Space & Gestalt Closure Principle | 负空间与格式塔闭合原则

The closure theorem from Gestalt psychology states that the mind tends to fill in missing information to see a complete shape. Design your negative space (the area around and between subjects) so it becomes an active participant.

格式塔心理学的闭合定理指出，大脑倾向于补全缺失的信息以看到完整形状。设计你的负空间（主体周围和之间的区域），使其成为积极的参与者。

The figure-ground relationship formula: a shape can be read as either figure or ground, but not both simultaneously. Use ambiguous edges to create double images.

图底关系公式：一个形状可以被解读为图或底，但不能同时解读。利用模糊边缘创造双重图像。

Rubin’s vase is the classic example: two profiles create a vase in the negative space. Practising this sharpens your ability to see and sculpt negative shapes.

鲁宾的花瓶是经典案例：两个侧面轮廓在负空间中形成一个花瓶。练习这能提高你观察和塑造负形的能力。

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9. Colour Temperature & Depth Formula | 色温与深度公式

Warm colours (red, orange, yellow) appear to advance toward the viewer, while cool colours (blue, green, violet) recede. This is the atmospheric perspective formula: warm forward + cool back = pictorial depth.

暖色（红、橙、黄）似乎向观者前进，而冷色（蓝、绿、紫）后退。这就是空气透视公式：暖色在前 + 冷色在后 = 画面深度。

In landscapes, distant hills become lighter, bluer, and less detailed. Replicate this: add white and a touch of blue to colours meant to sit in the distance.

在风景画中，远处的山丘变得更亮、更蓝、细节更少。复现这点：给本应位于远处的颜色加入白色和一抹蓝色。

A colour’s temperature is also relative; a violet can feel warm next to deep blue, cool next to red. Exploit these shifts to fine-tune spatial illusions.

颜色的温度也是相对的；紫罗兰色在深蓝旁边会感觉暖，在红色旁边会感觉冷。利用这些偏移可以精细调整空间错觉。

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10. Visual Rhythm & Repetition Formulas | 视觉节奏与重复公式

Rhythm in art is the repetition of shapes, colours, or lines. Regular rhythm (even spacing) creates calm; irregular rhythm (varying spacing) generates energy. The formula is: element × repetition + variation → rhythm.

艺术中的节奏是形状、颜色或线条的重复。规则节奏（均匀间距）营造平静；不规则节奏（变化间距）产生能量。公式为：元素 × 重复 + 变化 → 节奏。

Progressive rhythm, where an element gradually changes in size, colour, or spacing, suggests growth or movement. Think of a row of windows diminishing into the distance.

渐进节奏，即元素在尺寸、颜色或间距上逐渐变化，暗示生长或运动。想想一排向远处逐渐变小的窗户。

Create a repeating motif across your artwork, then break the pattern once to create an area of emphasis – this is the broken rhythm rule.

在作品各处创建重复母题，然后打破一次图案以创造强调区域——这就是破节奏法则。

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11. Texture & Pattern Interlocking Theorem | 纹理与图案交错定理

Texture can be actual (tactile) or implied (visual). The illusion of texture follows a formula: small, dense marks for rough surfaces; smooth, gradual blending for soft surfaces; crisp edges for sharp surfaces.

纹理可以是实际的（触觉）或隐式的（视觉）。纹理的错觉遵循一个公式：粗糙表面用小而密的笔触；柔软表面用平滑渐变的混合；锋利表面用锐利边缘。

Pattern interlocking – such as in Escher’s tessellations – uses translation, rotation, and reflection transformations to fill a plane. The underlying mathematical rule is that the shapes must fit together without gaps or overlaps.

图案交错——如埃舍尔的镶嵌——利用平移、旋转和反射变换来填满平面。其底层数学规则是形状必须拼合无间隙或重叠。

When designing a pattern, start with a simple geometric base: square grid, triangular grid, or hexagonal grid. Modify one tile and mirror the changes to the others.

设计图案时，从一个简单的几何基础开始：方形网格、三角形网格或六边形网格。修改一块砖片，并将变化镜像到其他砖片。

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12. The Creative Divergence-Convergence Formula | 创意发散-收敛公式

Creativity can be modelled as a two-phase process. The formula is: Divergent thinking (generate many ideas, no judgement) + Convergent thinking (select, refine, evaluate) → Strong final outcome.

创造力可以建模为一个两阶段过程。公式为：发散思维（生成大量想法，不加评判）+ 收敛思维（选择、提炼、评估） → 强大的最终成果。

In the divergent phase, use brainstorming lists, thumbnail sketches (try 20 small sketches in 10 minutes), and random word prompts to push past the obvious.

在发散阶段，使用头脑风暴列表、缩略图草图（尝试在 10 分钟内画出 20 个小草图）和随机词语提示，以突破显而易见的想法。

In the convergent phase, apply the composition formulas from this handbook: rule of thirds, value contrast, balance – to select the sketches with the strongest visual potential. Then iterate.

在收敛阶段，应用本手册中的构图公式：三分法、明度对比、平衡——来选择视觉潜力最强的草图。然后迭代。

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