test-repo/docs/.vitepress/theme/components/appendix/vlm-intro/LinearProjectionDemo.vue

<template>
  <div class="linear-projection-demo">
    <div class="demo-container">
      <!-- Step 1: Patch -->
      <div class="step-box">
        <div class="label">
          1. Patch (16×16×3) (示意 / Toy)
        </div>
        <div class="grid-patch">
          <div
            v-for="n in patchCellCount"
            :key="n"
            class="pixel"
            :style="{ backgroundColor: getPixelColor(n) }"
          />
        </div>
        <div class="desc">
          16×16 像素 × 3 通道 = 768 标量值
        </div>
      </div>

      <div class="arrow">
        ➜
      </div>

      <!-- Step 2: Flattened -->
      <div class="step-box">
        <div class="label">
          2. Flatten
        </div>
        <div class="vector-container">
          <div
            v-for="n in flattenSampleCount"
            :key="n"
            class="vector-cell"
            :style="{ backgroundColor: getPixelColor(n) }"
          />
          <div class="vector-ellipsis">
            …
          </div>
        </div>
        <div class="desc">
          得到 1×768 向量 (Vector)
        </div>
      </div>

      <div class="arrow">
        × W
      </div>

      <!-- Step 3: Projected -->
      <div class="step-box">
        <div class="label">
          3. Embedding
        </div>
        <div class="embedding-container">
          <div
            v-for="n in 8"
            :key="n"
            class="embed-cell"
          />
        </div>
        <div class="desc">
          映射到 D 维 (示意 D=8；常见 D=768)
        </div>
      </div>
    </div>
  </div>
</template>

<script setup>
const patchCellCount = 16 * 16
const flattenSampleCount = 32

const getPixelColor = (n) => {
  // Generate a gradient of colors
  const hue = (n * 20) % 360
  return `hsl(${hue}, 70%, 60%)`
}
</script>

<style scoped>
.linear-projection-demo {
  padding: 20px;
  background: var(--vp-c-bg-soft);
  border-radius: 6px;
  margin: 20px 0;
  overflow-x: auto;
}

.demo-container {
  display: flex;
  align-items: center;
  justify-content: space-around;
  min-width: 600px;
}

.step-box {
  display: flex;
  flex-direction: column;
  align-items: center;
  gap: 10px;
}

.label {
  font-weight: bold;
  font-size: 0.9em;
  color: var(--vp-c-text-2);
}

.desc {
  font-size: 0.8em;
  color: var(--vp-c-text-3);
}

.grid-patch {
  display: grid;
  grid-template-columns: repeat(16, 1fr);
  gap: 1px;
  width: 80px;
  height: 80px;
}

.pixel {
  width: 100%;
  height: 100%;
  border-radius: 2px;
}

.vector-container {
  display: flex;
  flex-direction: column;
  gap: 1px;
  height: 140px;
  width: 20px;
  justify-content: center;
}

.vector-cell {
  width: 100%;
  flex: 1;
}

.vector-ellipsis {
  font-size: 12px;
  line-height: 1;
  color: var(--vp-c-text-3);
  text-align: center;
  padding-top: 4px;
}

.embedding-container {
  display: flex;
  flex-direction: column;
  gap: 2px;
  height: 80px;
  width: 20px;
}

.embed-cell {
  width: 100%;
  flex: 1;
  background-color: var(--vp-c-brand);
  opacity: 0.8;
  border-radius: 2px;
}

.arrow {
  font-size: 1.5em;
  color: var(--vp-c-text-3);
  font-weight: bold;
}
</style>